The stellar populations of early-type galaxies – II

The stellar populations of early-type galaxies – II. The effects of environment and mass

Craig D. Harrison, Matthew Colless, Harald Kuntschner, Warrick J. Couch, Roberto De Propris, Michael B. Pracy
Research School of Astronomy & Astrophysics, Australian National University, Weston Creek, ACT 2611, Australia
Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile
Anglo-Australian Observatory, PO Box 296, Epping, NSW 2111, Australia
Space Telescope European Coordinating Facility, European Southern Observatory, Karl-Schwarzschild-Str, 85748 Garching, Germany
Centre for Astrophysics & Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia
E-mail: charrison@ctio.noao.edu
Accepted … . Received … ; in original form 2010 January 7
Abstract

The degree of influence that environment and mass have on the stellar populations of early-type galaxies is uncertain. In this paper we present the results of a spectroscopic analysis of the stellar populations of early-type galaxies aimed at addressing this question. The sample of galaxies is drawn from four clusters, with , and their surrounding structure extending to . We find that the distributions of the absorption-line strengths and the stellar population parameters age, metallicity and -element abundance ratio do not differ significantly between the clusters and their outskirts, but the tight correlations found between these quantities and velocity dispersion within the clusters are weaker in their outskirts. All three stellar population parameters of cluster galaxies are positively correlated with velocity dispersion. Galaxies in clusters form a homogeneous class of objects that have similar distributions of line-strengths and stellar population parameters, and follow similar scaling relations regardless of cluster richness or morphology. We estimate the intrinsic scatter of the Gaussian distribution of metallicities to be 0.3 dex, while that of the -element abundance ratio is 0.07 dex. The -folding time of the exponential distribution of galaxy ages is estimated to be 900 Myr. The intrinsic scatters of the metallicity and -element abundance ratio distributions can almost entirely be accounted for by the correlations with velocity dispersion and the intrinsic scatter about these relations. This implies that a galaxies mass plays the major role in determining its stellar population.

keywords:
galaxies: clusters: general – galaxies: elliptical and lenticular, cD – galaxies: stellar content – galaxies: formation.
pagerange: The stellar populations of early-type galaxies – II. The effects of environment and massReferencespubyear: 2010

1 Introduction

The classical model of galaxy formation, the monolithic collapse model (Eggen et al., 1962; Larson, 1974, 1975; Tinsley & Gunn, 1976; Arimoto & Yoshii, 1987; Bressan et al., 1994), proposes that galaxies form in a single massive collapse at high redshift and that subsequent evolution is purely passive. This model has been overtaken by the current dominant model of galaxy formation, the hierarchical merging model (Toomre, 1977; Searle & Zinn, 1978; White & Rees, 1978), which proposes that galaxies are built up through mergers: small objects form first and undergo a series of mergers that build up more massive objects. A third scenario, the revised monolithic collapse model (e.g. Merlin & Chiosi, 2006), proposes that galaxies form in a number of rapid mergers at high redshift before evolving passively.

Galaxy clusters originate from the most extreme density fluctuations, where galaxy formation and evolution is expected to proceed at an accelerated rate. Moreover, the stellar populations of galaxies moving into a cluster environment are expected to be modified via interactions with other galaxies and the dense intra-cluster medium. These interactions can be roughly divided into two broad classes: local processes including mergers (Toomre, 1977) and tidal interactions (Mastropietro et al., 2005); and global processes including ram pressure stripping (Gunn & Gott, 1972), interactions with the cluster tidal field (Bekki, 1999), harassment (Moore et al., 1999), and strangulation (Larson et al., 1980). Local processes are more efficient in galaxy groups, where relative velocities are lower, while global processes are more efficient in clusters where the frequency of interaction is higher.

Correlations are therefore expected between galaxy observables and environment (Kauffmann, 1996; Kauffmann & Charlot, 1998), and have been found for galaxy morphology (Davis & Geller, 1976; Dressler, 1980; Postman & Geller, 1984; Balogh et al., 1998), colour (Blanton et al., 2005), Sérsic index (Blanton et al., 2005; Hashimoto & Oemler, 1999), star-formation rate (Lewis et al., 2002; Gómez et al., 2003; Boselli & Gavazzi, 2006), and spectral type (Norberg et al., 2002). However, in a comprehensive study of the dependence of galaxy observables on environment within the SDSS, Blanton et al. (2005) suggest that the structural properties of galaxies are less dependent on environment than their masses and star-formation histories.

To add to this debate, Fundamental Plane studies have found no differences between field galaxies more massive than and their counterparts in clusters at the same redshift (Treu et al., 1999, 2001; van Dokkum et al., 2001), while less massive galaxies were found to be younger in the field (Treu et al., 2002; van Dokkum & Stanford, 2003; van der Wel et al., 2004, 2005; Treu et al., 2005a, b). This might imply that star formation in field galaxies occurs first in the most massive galaxies then progressively in less massive galaxies, and that mass rather than environment governs the overall growth.

The Lick system of absorption-line indices (Burstein et al., 1984; Faber et al., 1985; Burstein et al., 1986; Gorgas et al., 1993; Worthey et al., 1994; Trager et al., 1998) and associated models (e.g. Worthey, 1994; Thomas et al., 2003, 2004), from which the stellar population parameters (SPPs) age, metallicity ([Z/H]), and -element abundance ratio () can be estimated, provide an excellent method with which to study the role of mass and environment in determining galaxy properties.

The line-strengths of early-type galaxies are found to be correlated with velocity dispersion (). Lick indices that are more sensitive to [Z/H] effects, e.g. Mgb, are positively correlated (Burstein et al., 1988; Bender et al., 1993; Ziegler & Bender, 1997; Colless et al., 1999; Kuntschner, 2000) while those indices more sensitive to age effects, e.g. , are negatively correlated (Fisher et al., 1995; Fisher et al., 1996; Jørgensen, 1997, 1999a; Kuntschner, 2000; Caldwell et al., 2003; Bernardi et al., 2003). Although both elements are sensitive to [Z/H], the slope of the correlation between Mg and velocity dispersion is found to be much steeper than that of Fe (Worthey et al., 1992; Fisher et al., 1995; Greggio, 1997; Jørgensen, 1999a; Kuntschner, 2000; Terlevich & Forbes, 2002).

These index– correlations suggest that the SPPs should also be correlated with velocity dispersion. Given the difference in the slopes of the Mg– and Fe– relations, a correlation between and velocity dispersion was expected and has been confirmed (Trager et al., 2000a; Proctor & Sansom, 2002; Thomas et al., 2002; Mehlert et al., 2003; Thomas et al., 2005). If the -element enhancement is due to the timescale of star formation, and velocity dispersion is a proxy for mass, then this correlation indicates that more massive galaxies form their stars on shorter timescales than less massive galaxies.

The [Z/H] of a galaxy is also found to correlate with velocity dispersion (Greggio, 1997; Thomas et al., 2005), with massive galaxies being more metal-rich. Such a relation is a natural consequence of galactic wind models (e.g. Arimoto & Yoshii, 1987), which show that the larger gravitational potential of massive galaxies allows them to better retain their heavy elements.

Whether a correlation exists between age and velocity dispersion is still uncertain. Early studies found no significant correlation (Trager et al., 2000a; Kuntschner et al., 2001; Terlevich & Forbes, 2002), but recent studies have detected a weak but significant correlation having large scatter (Proctor & Sansom, 2002; Proctor et al., 2004a; Proctor et al., 2004b; Thomas et al., 2005), with more massive galaxies being older. This trend, which would indicate that more massive galaxies formed their stellar content earlier, is in agreement with the concept of down-sizing (Cowie et al., 1996) and the latest semi-analytic models of galaxy formation (e.g., De Lucia et al., 2006).

Early-type galaxies in low-density environments exhibit small differences to those in clusters: at a given luminosity, the early-type galaxies in low-density regions are Gyr younger and dex more metal-rich than those in clusters (Trager et al., 2000a; Poggianti et al., 2001; Kuntschner et al., 2002; Terlevich & Forbes, 2002; Caldwell et al., 2003; Proctor et al., 2004a; Thomas et al., 2005; Sánchez-Blázquez et al., 2006). In conflict with the above results, Gallazzi et al. (2006), using a large sample of early-type galaxies from the SDSS, found evidence that galaxies in low-density environments were less metal-rich than those in high-density environments. Intriguingly, there appears to be no environmental dependence of (Kuntschner et al., 2002; Thomas et al., 2005), indicating that star formation in galaxies of a given mass occurs on the same timescale whether they are located in high-density or low-density environments.

While it appears that the stellar populations of galaxies change from low-density environments to high-density environments, the density threshold at which this change occurs is uncertain. Studies of the star-formation rate of galaxies in and around clusters (Lewis et al., 2002; Gómez et al., 2003) find an increase in the star-formation rate with increasing distance from the cluster centre, converging to the mean field rate at distances greater than . The critical projected density at which suppression of star-formation begins is uncertain but the environmental influences on galaxy properties are believed not to be restricted to cluster cores, being effective in all groups where the density exceeds the critical value. The observed low rates of star formation well beyond the virialised cluster rule out physical processes associated with extreme environments (such as ram pressure stripping of disk gas) being completely responsible for the variations in galaxy properties with environment.

This paper is the second in a series of papers aimed at studying the effects of environment and mass on the stellar populations of early-type galaxies. The first paper described our sample selection, observations, data reductions, and method of measuring line-strengths and estimating stellar population parameters within the framework of the Lick system. In this paper we present the results of this study utilising data from four clusters and their surrounds. The data extends to , allowing us to probe the in-fall regions of the clusters, which to date have been poorly studied. The layout of the remainder of the paper is as follows. §2 briefly describes the sample, observations and reductions, measurement of Lick indices and SPP estimation. Analysis of the absorption-line strengths is detailed in §3 and the distributions of the SPPs in §4. The correlations between the SPPs and velocity dispersion are discussed in §5 while the contribution from these correlations to the intrinsic scatter in the parameter distributions are investigated in §6. We discuss the results of this study in §7 and present a summary of the work in §8.

A Hubble parameter km s Mpc, matter density parameter and dark energy density parameter are adopted throughout this work.

2 From Observations to Stellar Population Parameters

Details of the observations, data reductions, measurement of Lick indices and estimation of the corresponding SPPs are given in Harrison et al. (2010, submitted; hereafter referred to as Paper I). Therefore only brief descriptions will be given here.

Observations of galaxies from four clusters (A930, A1139, A3558 and Coma) of varying richness and morphology were made with 2dF during the nights of 19–21 April 2002. Observations of galaxies from the same four clusters and the structures around them were made with 6dF during the nights of 6–8 March 2003. The 6dF sample contained some galaxies in common with the 2dF sample, but mostly consisted of galaxies in the outer regions of each cluster. In two of the fields (A1139 and A930), the observations were offset from the cluster centre, allowing galaxies with cluster-centric distances of up to Mpc to be studied. The set-up of the two instruments can be found in Paper I.

A brief discussion of the way galaxies were classified as early types or not is warranted here. This was done spectroscopically with galaxies that showed signs of H (EW Å) or [OIII]5007 Å (EW Å) emission being classified as star forming. We chose to classify a galaxy by its spectrum because comparisons to SSP models are (almost) meaningless in galaxies with significant emission. In-fill of the absorption feature by nebular emission results in weaker line-strengths and incorrectly older ages. Some methods used to correct for this nebular in-fill (e.g. Gonzalez, 1993; Trager et al., 2000a, b) have proved unsatisfactory, while others (Sarzi et al., 2006) can only correct for relatively weak emission. For these reasons we eliminated all galaxies with signs of emission from our sample of early types. It must be noted that, in doing so, it is possible that we exclude from our stellar population analysis early-type galaxies that have had star formation triggered by the cluster environment.

Other methods of classifying galaxies are not problem-free. Classifying by morphology is highly subjective and samples selected by colour-magnitude cuts still contain contamination by galaxies that would have been morphologically classified as late types. More importantly, these methods do not eliminate all emission-line galaxies, up to 30% of red sequence galaxies can show signs of LINER emission (Graves et al., 2007), and so the interpretation of a stellar population analysis for these galaxies would be difficult.

However, the absence of emission lines does not guarantee that a galaxy has not had significant star formation in its recent past and so it is possible that our sample of early types contains a small number of post-starburst galaxies. The intrinsic scatters in the line strength– (Section 3.1) and stellar population parameter– relations (Section 5.1) are comparable to published results implying that if our sample contains recently star-forming galaxies then it is in no greater number than previous samples.

The basic reduction steps, such as bias subtraction, spectrum extraction, flat-fielding, wavelength calibration, fibre throughput determination and correction, and sky subtraction, were performed with the purpose-built data reduction packages 2dfdr (Colless et al., 2001) and 6dfdr (Jones et al., 2004). Redshifts were measured using the program runz (Colless et al., 2001) while the IRAF task fxcor was used to measure velocity dispersions.

Line-strengths were measured and transformed to the Lick system closely following procedures outlined in a number of papers (e.g. Gonzalez, 1993; Fisher et al., 1995; Worthey & Ottaviani, 1997; Trager et al., 1998; Kuntschner, 2000). The spectra were broadened to the Lick resolution ( 9 Å FWHM), and the line-strengths were measured using the program indexf (Cardiel et al., 1998).

A number of corrections were then applied to the measured line-strengths to fully calibrate them to the Lick system. These corrections include a velocity dispersion correction to account for the change in line-strength caused by velocity broadening, an aperture correction to account for the different linear sizes subtended by the different fibres at different redshifts, and, finally, applying any offsets that may arise due to the fact that the Lick spectra were not flux calibrated. This resulted in the measurement of the line-strength indices C4668, , , [OIII], [OIII], Fe5015, Mg, Mg, Mgb, Fe5270, Fe5335 and Fe5406 of the stellar populations within the inner kpc of each galaxy.

The age, [Z/H], and of a galaxy were obtained by comparing our measured line-strengths to the models of Thomas et al. (2003) and accepting the combination of SPPs of the model with the smallest (Proctor et al., 2004b). We interpolate the models logarithmically in steps of 0.02 dex in age and [Z/H], and 0.01 dex in . Errors on the parameters were estimated by using the constant boundaries as confidence limits (see Press et al., 1992).

In summary, we measured velocity dispersions, redshifts, and line-strengths for a total of 416 galaxies: 158 of these are early-type galaxies from Coma, A1139, A3558, or A930 that are located within the Abell radius (i.e. at a projected radial distance Mpc) and comprise our cluster sample; 87 are early-type galaxies from the outskirts of these clusters at projected radial distances Mpc and comprise the cluster-outskirts sample; 168 galaxies were deemed to be star-forming, and make up the emission-line sample; the 3 remaining galaxies lacked the information necessary to classify them as either an early-type or emission-line galaxy. Of these 416 galaxies SPPs were estimated for 219; 142 in the cluster sample and 77 in the cluster-outskirts sample.

3 Absorption-Line Analysis

3.1 Line-strength– relations in cluster early-type galaxies

Index Zero-point Slope Probability
0. 546 1.000
. 479 1.000
. 442 1.000
0. 284 0.999
0. 626 1.000
0. 662 1.000
0. 675 1.000
0. 342 0.999
0. 352 1.000
0. 166 0.921
Table 1: The line-strength– fits, Spearman rank correlation statistics, probabilities of a correlation, and the intrinsic scatter (; in mag) for the cluster galaxies.

In early-type galaxies the strengths of certain absorption features are observed to be correlated with velocity dispersion. Such correlations are important as they provide links between a galaxy’s dynamical and chemical evolution; i.e. between galaxy mass, metallicity, and abundance ratios.

Historically, the Mg– relation was studied using Mg, which is measured in magnitudes of absorbed flux. More recent studies (e.g. Colless et al., 1999; Kuntschner et al., 2001) have used Mgb, which is a more reliable index, as it is narrower, but is measured as an equivalent width in Å. These studies converted indices measured in equivalent widths to magnitudes (for the conversion see Colless et al., 1999), primarily to allow comparison with older studies that used Mg. We continue this practice and indices that have been converted to magnitudes will be denoted with a prime symbol (e.g. Mgb).

The variations of the index line-strengths with velocity dispersion for the cluster sample are shown in Figure 1. These plots contain the combined data from all four clusters, as Kolmogorov-Smirnov (KS) 2D two-sample tests indicate consistency of the line-strength– distributions between clusters, in that most distributions differed only at the 1–2 level. That these relations are found to be consistent in the four clusters, which span the ranges of Abell richness classes and Bautz-Morgan (BM) morphologies, is remarkable. This suggests that the cluster environment has little effect on the line-strengths of early-type galaxies (see Colless et al. (1999) for a study of the Mg– relation as a function of cluster environment). Table 1 shows the results of linear fits to the data, accounting for errors in both quantities, along with the Spearman rank correlation statistic (), the probability that the two quantities are correlated and the estimated intrinsic scatter about each relation.

We assume the intrinsic scatter about these relations is Gaussian and estimate it by maximising the logarithmic likelihood

(1)

where the are the residuals to the fit for index and , where and are the individual errors on the index and , is the slope of the relation for index , and is the estimated intrinsic scatter. These estimated intrinsic scatters are listed in Table 1.

With the exception of Fe5406, correlations are found at confidence level for all indices. Strong correlations () are found for C, Mg, Mg and Mgb, while a weak correlation () is found for Fe5015. Except for and , which are moderately anti-correlated, all other indices are moderately correlated. The slope of the fit to the Fe5406 data is very flat and consistent with being zero. and are the only indices used here that are more sensitive to age effects and the only ones that exhibit an anti-correlation; all the other indices are more sensitive to [Z/H] effects and either exhibit a positive correlation or no correlation.

Young stellar populations exhibit strong Balmer absorption features, which weaken with age. Therefore, a simple interpretation of the anti-correlation of and with velocity dispersion is that more massive galaxies are older. The simple interpretation of the positive correlation between the metal-sensitive indices and velocity dispersion is that more massive galaxies are more metal-rich. The usual explanation of this trend is that massive galaxies are better able to retain their heavy elements due to their larger gravitational potential, a scenario that arises naturally in galactic wind models (e.g. Arimoto & Yoshii, 1987). Alternatively, a variable IMF could lead to a similar mass-[Z/H] relation. Koeppen et al. (2007) have developed a model where the effective upper mass limit of stars is lower in galaxies with a low star-formation rate. This reduces the number of SNII, and hence the [Z/H], in low mass galaxies and leads to a similar mass-[Z/H] relation.

Figure 1: The variations (in magnitudes) of the index line-strengths with velocity dispersion for the cluster sample. Most indices exhibit a tight relation with strong correlations found for C4668, Mg, Mg and Mgb, while and exhibit moderate anti-correlations.
Reference C4668 Fe5015
Zero-point Slope Zero-point Slope Zero-point Slope
This study . 0530.009 0. 0670.004 0. 1670.009 . 0440.004 0. 0460.008 0. 0130.003
Kuntschner (2000) . 1100.042 0. 0900.018 0. 1060.015 . 0200.007 0. 0020.019 0. 0360.008
Nelan et al. (2005) 0. 0750.002 . 0410.001 0. 0150.001
Clemens et al. (2006) 0. 0440.003 0. 0250.003 0. 2270.002 . 0710.002 0. 1270.002 . 0230.002
Sánchez-Blázquez et al. (2006) . 0710.018 0. 0670.008 0. 0870.009 . 0120.004 0. 0250.011 0. 0210.005
Ogando et al. (2008) 0. 1560.013 . 0420.006 0. 0530.010 0. 0110.004
Matković et al. (2009) . 0440.014 0. 0600.014 0. 1160.009 . 0240.009 0. 0600.007 0. 0050.007
Reference Mg Mg Mgb
Zero-point Slope Zero-point Slope Zero-point Slope
This study . 2850.018 0. 1800.008 . 4020.032 0. 2990.014 . 1300.012 0. 1290.005
Kuntschner (2000) . 1580.035 0. 1360.015 . 1270.054 0. 1910.023 . 0560.044 0. 1020.020
Nelan et al. (2005) 0. 1210.003 0. 1890.003 0. 1340.002
Clemens et al. (2006) . 2450.010 0. 1630.004 . 1980.013 0. 2080.006 . 1550.007 0. 1420.007
Sánchez-Blázquez et al. (2006) . 0500.019 0. 0910.008
Ogando et al. (2008) . 1590.020 0. 1310.009 . 1530.029 0. 1940.013 . 0950.018 0. 1120.008
Matković et al. (2009) . 2040.036 0. 1410.017 . 1430.045 0. 1780.020 . 0230.015 0. 0800.015
Reference Fe5270 Fe5335 Fe5406
Zero-point Slope Zero-point Slope Zero-point Slope
This study 0. 0440.008 0. 0160.004 0. 0080.011 0. 0280.005 0. 0430.011 0. 0100.005
Kuntschner (2000) 0. 0240.020 0. 0290.009 . 0170.020 0. 0430.009 0. 0230.026 0. 0230.012
Nelan et al. (2005) 0. 0170.001 0. 0230.001 0. 0180.001
Clemens et al. (2006) 0. 0850.003 . 0010.003 0. 0140.003 0. 0270.003 . 0020.003 0. 0310.003
Sánchez-Blázquez et al. (2006) 0. 0270.007 0. 0240.003 . 0010.013 0. 0350.006
Ogando et al. (2008) 0. 0490.008 0. 0150.004 0. 0290.009 0. 0200.004 0. 0340.009 0. 0180.004
Matković et al. (2009) 0. 0920.009 . 0070.009 0. 0690.008 0. 0010.008
Table 2: A comparison of the line-strength– relations to those found in the literature.

We compare our line-strength– relations to various estimates from the literature in Table 2. These estimates are based on a sample of early-type galaxies from the Fornax cluster (Kuntschner, 2000), a sample of red-sequence galaxies from numerous low- clusters (Nelan et al., 2005), a magnitude-limited sample of early-type galaxies drawn from the SDSS (Clemens et al., 2006), a sample of early-type galaxies in high-density environments (Sánchez-Blázquez et al., 2006), a magnitude-limited sample of early-type galaxies in high-density environments (Ogando et al., 2008), and a sample of early-type galaxies from the core of the Coma cluster (Matković et al., 2009).

Generally, our results compare well with those in the literature. We find that in the majority of cases the slopes agree at the level or better. Of those comparisons that disagree by more than , we note that almost half are comparisons to the estimates of Clemens et al. (2006) and the rest consist almost entirely of comparisons of Mg and Mg.

The discrepancy with Clemens et al. (2006) possibly arises due to differences in the aperture corrections applied to each dataset. We correct our line-strength measurements to fixed physical size of kpc, independent of the velocity dispersion of the galaxy. The correction applied by Clemens et al., however, is to a physical size of /10 and is a function of velocity dispersion. Confusing the issue is the fact that some of their slopes are steeper than ours (e.g. Fe5406), some are shallower (e.g. C4668) and some are in the opposite sense (e.g. Fe5015).

The discrepancy between our estimated slopes of Mg and Mg and those in the literature is a little easier to understand. Both these indices have very broad definitions and so their line-strengths are highly-sensitive to the shape of the continuum. The fact that we divided out our continuum is probably the reason for this discrepancy. This is one of the reasons why we excluded these two indices from our fits to the models in estimating the SPPs (see Section 6 in Paper I).

Most comparisons with Matković et al. (2009) agree at better than the level, the exceptions being Mg and Mgb, but since both samples include early-types from the core of the Coma cluster it is worthwhile to make a direct comparison of these galaxies alone. Overall, this results in better agreement between the slopes, although the change is almost negligible in most cases. Three indices (C4668, Fe5270 and Fe5335) show worse agreement but the largest change in significance is only 0.24. All other indices show better agreement; again, most changes are small except in the case of where the significance changes by 1.38 from 2.03 to 0.65.

The intrinsic scatters found for our line-strength– relations are given in Table 1. Most of our estimates agree well with those of Kuntschner (2000) and Sánchez-Blázquez et al. (2006), with perhaps the exceptions of , Fe5015, Fe5270 and Fe5335. We find an intrinsic scatter in of 0.008 mag (as does Sánchez-Blázquez et al.), which is double that of Kuntschner. For the three Fe indices, our scatters are larger than those found by Sánchez-Blázquez et al. who find negligible-to-no scatter in these relations. Our estimates for these indices are in good agreement with that of Kuntschner, except for Fe5335 for which we find almost double the scatter of that found by this author (0.008 mag compared to 0.005 mag).

Figure 2: The variations (in magnitudes) of the index line-strengths with velocity dispersion for the cluster-outskirts sample. The solid line is the linear fit to the data while the dashed red line is the fit to the cluster sample. The slopes of all relations are consistent with those found in the cluster sample.

Given that the galaxies from this study are drawn from four different clusters, with varying richness classes and BM classifications, the small intrinsic scatters about the line-strength– relations is truly remarkable, and implies that the stellar populations in cluster early-type galaxies are homogeneous. This result agrees with that of Colless et al. (1999), who found no correlation between the Mg– zero-point and cluster velocity dispersion, X-ray luminosity, or X-ray temperature (see also Bernardi et al., 1998; Worthey & Collobert, 2003; Sánchez-Blázquez et al., 2006). For galaxies in clusters, Jørgensen et al. (1996) found that the Mg– residuals are weakly correlated with local density. However, since the residuals are correlated with cluster velocity dispersion and not projected cluster-centric distance, the interpretation is of a correlation between the Mg– zero-point and cluster mass, albeit a weak one.

3.2 Line-strengths– relations in the cluster-outskirts

Using the wide field of 6dF and, in the cases of A1139 and A930, offsetting the field centres with respect to the cluster centres allowed us to obtain data on galaxies well outside the clusters. We obtained line-strengths of galaxies out to a projected cluster-centric radius of Mpc, which corresponds to . We note that the average distance between Abell clusters is Mpc.

Index Zero-point Slope Probability
0. 260 0.985 0.3
. 275 0.988 0.0
. 322 0.997 1.2
0. 086 0.413 0.4
0. 748 0.995 0.8
0. 650 0.978 0.6
0. 392 1.000 1.3
0. 410 0.814 0.7
0. 548 0.990 0.0
0. 405 0.939 0.5
Table 3: The line-strength– fits, Spearman rank correlation statistics (), probabilities of a correlation, and intrinsic scatters (; in mag) for galaxies in the cluster-outskirts sample. The number of standard deviations by which the slopes of the cluster-outskirts sample relations differ from the cluster sample relations () is given in the last column.

The trends with velocity dispersion of the line-strengths in the cluster-outskirts sample (i.e. those galaxies outside ) are shown in Figure 2. The solid line in each panel is our linear fit to the data (accounting for errors in both quantities) while the dashed line is the fit to the cluster galaxies. In Table 3 we list the details of the fits, the Spearman rank correlation statistics, the probabilities of a correlation and the estimated intrinsic scatters about the relations. The last column in this table shows the number of standard deviations by which the slopes of the cluster-outskirts sample relations differ from the cluster sample relations; all indices are found to have slopes consistent with those found for galaxies in the cluster sample. However, the only indices that show correlations significant at the level in the cluster-outskirts sample are Mgb and , and while the strength of the correlation remains the same for it is reduced for Mgb from a strong correlation in the cluster sample to a moderate correlation here.

The change in the Fe indices is interesting. Fe5015 changes from being weakly correlated in the cluster sample to uncorrelated in the cluster-outskirts sample. The other three Fe indices remain moderately-to-weakly correlated (although with reduced significance) but their slopes are all consistent with being zero. In the cluster sample only Fe5406 had a slope that was consistent with being zero. In addition all four Fe indices have decreased intrinsic scatters about their fits, as does Mg. C, , and Mgb all show an increase in the intrinsic scatter, while for Mg it remains the same.

There appears to be a large number of galaxies that have low index strengths compared to those expected from the relations found in the cluster sample. For Fe5015 the spread is consistent with what is found in the cluster sample. The galaxies with low and strengths, which also are found in the cluster sample but in smaller numbers, are possibly those that suffer from nebular in-fill. Most of the galaxies in the cluster-outskirts sample were observed with 6dF and so have no details of H emission because the wavelength coverage was insufficient. Therefore, it is not unexpected that the level of this possible contamination by star-forming galaxies in this sample is slightly higher than in the cluster sample.

In the cases of and Mgb, there does appear to be a real sub-population of galaxies that are genuinely offset from the relations found in the cluster sample, having weaker line-strengths for a given velocity dispersion. This is possible if galaxies in clusters find it easier to retain their heavier elements than those in their outskirts, due to the dense intra-cluster medium retarding the development of galactic winds and the expulsion of the heavier elements.

Another possibility is that the weakened line-strengths are caused by the aperture correction. Early type galaxies exhibit strong metallicity and age gradients (e.g. Davies et al., 1993) and indices measured in massive galaxies will sample a smaller fraction of the effective radius than those in less massive galaxies. If lower mass galaxies are found preferentially in the cluster outskirts then this could lead to a change in the relations in the two regions. These aperture corrections are necessary to allow a fair comparison between galaxies in clusters at different redshifts and between galaxies in the same cluster but observed with fibres that subtend different angles (2dF and 6dF). However, we do not find that lower mass galaxies are preferentially found in the cluster-outskirts sample. In fact, while the distributions of magnitudes are similar in shape in both regions (because we deliberately targeted brighter galaxies), the peak of the distribution in the core is shifted to fainter magnitudes relative to the outskirts sample by  mag, i.e. on average the cluster-outskirts galaxies are brighter. Therefore this can not be the reason for the weakening of the relations.

3.3 The radial distribution of star-forming galaxies in clusters

In the analyses so far, the included galaxies were limited to those that showed no significant sign of on-going star formation, as determined from H or [OIII]5007Å emissions. This allows us to be reasonably confident that their absorption feature is free from in-filling caused by nebular emissions. However, from these previously excluded galaxies we can determine where in the cluster and its surrounds star-forming galaxies reside.

In the left panel of Figure 3 we show, for our entire sample of galaxies, the line-strengths as a function of projected cluster-centric distance. Circles represent galaxies that are classified as early-types, while crosses represent emission-line galaxies (and were up to this point excluded from our analysis). The distribution of line-strengths forms a ridge at Å. Most of the galaxies with line-strengths weaker than Å are those classified as emission-line galaxies, although a few galaxies classified as early-types also lie below this ridge line. It is possible that these galaxies have weak due to in-filling and yet show no significant sign of [OIII]5007Å emission. This confirms that while correcting for emission by the strength of the [OIII]5007Å emission line (Gonzalez, 1993; Trager et al., 2000a, b) may be acceptable in a statistical sense, it is not reliably applicable to individual galaxies, which may show moderate to strong emission and little or no [OIII]5007Å emission (Nelan et al., 2005).

Figure 3: Left: The variation in line-strength as a function of projected cluster-centric radius. Circles represent early-type galaxies and crosses represent galaxies that are classified as emission-line galaxies. The red line shows how the mean line-strength changes with radius and indicates that on average galaxies in the outskirts of clusters are Å weaker in than those in the centre of clusters. The blue line shows how the line-strength evolves in a galaxy as it ages after an instantaneous burst of star formation (the direction is given by the blue arrow; see text for details). Right: The fraction of galaxies with Å as a function of projected cluster-centric radius.

Figure 3 shows an increasing scatter in line-strengths with increasing radius. Not only is there a scatter to lower values (an indication of older ages or possibly in-filling in galaxies that have experienced recent star formation), there is also a scatter to higher values, and thus younger ages, for early-type galaxies. The red line in the left panel of Figure 3 shows how the mean H line-strength (calculated for galaxies within a 0.4 dex radius bin at steps of 0.05 dex) changes with radius. We see that within a radius of Mpc (i.e. ) the mean value is a constant ( Å), while outside this radius it steadily decreases to a value of Å. Since the oldest isochrone (15 Gyr) in the Thomas et al. (2003) models has strengths –2 Å we conclude that these low line-strengths, for the galaxies classified as early types, represent nebular in-fill in recently star-forming galaxies, which are preferentially found in the outer regions of the cluster environment. This conclusion is consistent with a previous study of galaxy star-formation rate and environment by Lewis et al. (2002), which found increasing star-formation rates with increasing distance from the cluster centre that converge to field rates at distances greater than (see also Gómez et al., 2003; Kauffmann et al., 2004).

The distribution of galaxies in this figure can be thought of as tracking the evolution of a star-forming galaxy. A galaxy falling into the cluster undergoes a burst of star formation, which shifts the galaxy to emission (i.e. negative line-strengths). As the episode of star formation progresses and the galaxy moves deeper into the cluster, the galaxy gradually shifts to stronger absorption (positive line-strengths). Then, once star formation has ceased, the galaxy settles back onto the ridge. This evolution is represented schematically by the blue line in the figure. The dotted segment of the line represents the galaxy as it moves from being a star-forming galaxy to a post-starburst galaxy (the emission line-strengths are indicative only). The solid segment of the line shows how, according to the Thomas et al. models, the line-strength changes in a galaxy with [Z/H]=0.35 dex and =0.2 dex as it ages from 1 Gyr to 15 Gyr. The mapping between projected cluster-centric radius and time is arbitrary. This figure is similar to Figure 10 in Couch & Sharples (1987), which shows the evolutionary track of a star-bursting galaxy in H–colour space.

The right panel of Figure 3 shows the fraction of galaxies (in the same bins as used for calculating the mean in the left panel) that have line-strengths less than 1.4 Å. In the core of the cluster none of the galaxies fall below this value, while at large radii the fraction increases rapidly to the limit of our data, where of galaxies have line-strengths less than this value. We conclude that the cluster core is relatively free from young galaxies and galaxies that have experienced recent star formation, and that these galaxies are found more commonly outside .

4 Stellar Population Parameter Distributions

4.1 The cluster distributions

Figure 4: The distributions of the SPPs for all galaxies in the cluster sample. Marginal distributions are shown for each parameter and the dotted lines show the median values of each parameter. Galaxies from Coma are shown as blue circles, from A1139 as green squares, from A3558 as yellow triangles and from A930 as red crosses.

The distributions of SPPs from the four clusters combined are shown in Figure 4. Marginal distributions are plotted for each of the parameters and the median values are marked as dotted lines. Galaxies from Coma are shown as blue circles, from A1139 as green squares, from A3558 as yellow triangles and from A930 as red crosses. Errors are shown for individual galaxies but two points must be kept in mind. Firstly, the age and [Z/H] errors are correlated and so the error bars here do not accurately reflect the true shape of the confidence contours. For the two other combinations of parameters the errors are much less correlated and so the error bars are a good representation of the confidence contours (see Paper I). Secondly, a galaxy’s error estimate cannot be larger than its distance to the edge of the model grid. This is only an issue for age estimates since we quote two-sided errors. So, if a galaxy’s error bar reaches 15 Gyr it should be considered a lower limit only.

Looking at the distributions as a whole, we note that very few galaxies have [Z/H] less than solar with most having dex. Similarly, is mostly greater than solar and lies in the range dex. The bulk of the galaxies have old ages and almost all lie in the range Gyr. The distributions we find for the cluster sample are in general agreement with those found by previous authors (e.g. Gonzalez, 1993; Jørgensen, 1999a; Kuntschner, 2000; Trager et al., 2000b; Poggianti et al., 2001; Thomas et al., 2005; Collobert et al., 2006).

Looking at the SPP distributions of each cluster individually we find few differences. The median values and errors for the SPPs in each cluster are given in Table 4. The errors on the median values were estimated from Monte Carlo bootstrap simulations in the following manner. For each galaxy in a cluster, we randomly draw index values from the galaxy’s index error distributions, using the same set of indices that were used to estimate the parameters originally. These index values are then converted to parameter estimates and the median values are determined. This process is repeated 10,000 times and the RMS errors on the median values are computed.

Cluster [Z/H] Age
Coma   6 5
A1139 8
A3558 6 1
A930 8
Table 4: The median SPP values for each cluster and the number of galaxies for which the parameters were measured.

The distributions of SPPs from cluster-to-cluster show remarkable similarity, with no significant differences between the median values of any of the four clusters. However, to conclusively detect any differences in the age and [Z/H] distributions, a two-sample 2D KS test is required, due to the correlated errors between age and [Z/H]. For the distributions a two-sample 1D KS test is sufficient. The results of these tests are that the joint distributions of age and [Z/H], and the distributions of in each of the four clusters are consistent with each other.

Looking at the combined distributions of the cluster sample (142 galaxies in total), we find that the median [Z/H] is dex, the median age is Gyr, and the median is dex. The errors on these median values were determined the same way as for the clusters individually. These median values are shown as dotted lines in the marginal distributions in Figure 4.

There are some galaxies that have line-strengths that fall outside the ranges predicted by the stellar population models, in that there are six galaxies with age=15 Gyr, four with [Z/H]=0.59 dex, and two with =–0.19 dex. Two galaxies have more than one parameter on the edge of the models and so in total there are 10 such galaxies. These galaxies are assigned the combination of SPPs that most nearly fits the combination of line-strengths, as mentioned in Paper I. It is hard to determine the origin of this difference between the data and the models, which could be due to errors in the stellar population models (it should be noted that the models provide no estimate of systematic uncertainties), or due to errors in the observations or data reduction; only a small percentage of galaxies are affected, with of galaxies having self-consistent model parameter fits.

For the galaxies with age=15 Gyr, it is possible that some of these galaxies are affected by nebular emission, despite the fact that care was taken in eliminating such galaxies. As was noted in Paper I, it is possible for galaxies to have in emission and no detectable [OIII]5007Å (Nelan et al., 2005). If this emission is undetectable, because it is swamped by absorption, and there is no [OIII]5007Å emission, then such a galaxy will not be classified as an emission-line galaxy and will not be excluded from the cluster sample.

Figure 5: The distributions of the SPPs, estimated from , Mgb and Fe5335 only, for all galaxies in the cluster sample. The dotted lines show the median values of each parameter.

It is also evident that there appears to be an anti-correlation between [Z/H] and age, in the sense that younger galaxies are more metal-rich. This might in principle be due to the non-orthogonal nature of the [Z/H]-age grids produced by the stellar population models, which mean that the errors on these two quantities are correlated. The effect is that an increase in a [Z/H]-sensitive index results not only in a increase in [Z/H] but also in a decrease in age; correspondingly, an increase in an age-sensitive index results in a decrease in age and an increase in [Z/H]. Due to the irregular shape of the grid, this effect varies with location over the grid.

That a degree of anti-correlation between age and [Z/H] is introduced by the correlated errors is not disputed; however, whether this accounts for the anti-correlation entirely is still contentious (Colless et al., 1999; Jørgensen, 1999a; Trager et al., 2000a; Poggianti et al., 2001; Kuntschner et al., 2001; Terlevich & Forbes, 2002; Proctor & Sansom, 2002; Bernardi et al., 2005; Sánchez-Blázquez et al., 2006). Some studies find that there exists a moderate anti-correlation over and above that introduced by the errors (e.g. Colless et al., 1999) while others find that no correlation exists once the errors are taken into account (e.g. Kuntschner et al., 2001). To determine whether the anti-correlation between age and [Z/H] is real or not, we perform a simple test which involves comparing the degree of anti-correlation in the observed joint age–[Z/H] distribution with those obtained by Monte Carlo simulations.

Due to the need for an automated process to convert SPPs to line-strengths (and vice versa) it is not feasible to use the method of SPP estimation that makes use of all available indices. Therefore, for this exercise, we rely on only three indices , Mgb and Fe5335. Combinations of these three indices are commonly used in line-diagnostic diagrams to estimate SSPs. With this combination of indices, the age distribution is approximately exponential and both the [Z/H] and distributions are approximately Gaussian (see Figure 5).

We start by generating a sample of galaxies with age, [Z/H], and estimates (parameter triples); the [Z/H] and were drawn from the distributions defined by the medians of the observed values and their intrinsic scatters and the age was drawn from an exponential distribution (see Section 6 for details on how the intrinsic scatters and the -folding of the exponential age distribution were determined). These parameter triples are then converted to , Mgb, and Fe5335 index values (index triples), which are then perturbed using the observed indices error distributions. These perturbed index triples are then converted back to parameter triples and the Spearman rank correlation statistic is calculated for age and [Z/H]. This procedure is carried out 10,000 times. From these Monte Carlo simulations we determine the probability of obtaining by chance a correlation greater than that found for the observed data, and we find that there exists a real anti-correlation between age and [Z/H] (over and above the error-induced correlation) that is significant at the level.

4.2 The distributions in the cluster-outskirts

Figure 6: Comparison of the SPPs in the cluster-outskirts sample (black circles) to those in the cluster sample (red crosses). The marginal distributions for the cluster sample are shown as open histograms and for the cluster-outskirts sample as black histograms. The dashed line in the marginal distributions represents the median parameter values in the cluster-outskirts sample and the dotted line that of the cluster sample.

The distributions of SPPs in the cluster-outskirts sample (red crosses) are compared to those from the clusters (black circles) in Figure 6. For the sake of clarity, only the errors for the cluster-outskirts sample are shown. The dashed lines in the marginal distributions are the median galaxy parameters for the cluster-outskirts sample and the dotted lines are for the cluster sample. The galaxies in the cluster-outskirts sample have a median [Z/H] of dex, a median age of Gyr, and median of dex. Compared to the combined cluster sample we detect no difference in the median values for the galaxy parameters, although the errors are substantial.

Looking at the distributions we see that there is very little difference between the galaxies in this sample and those in the clusters, an assessment that is confirmed by KS testing (a two-sample 2D KS test in the case of the age and [Z/H] distributions and a two-sample 1D KS test for the distributions).

The fact that the distributions are the same in the clusters and their outskirts is intriguing, given that the cores of galaxy clusters are thought to result from regions of high over-density where the process of star formation occurs rapidly (Kauffmann & Charlot, 1998; Schindler et al., 2005; Romeo et al., 2005; De Lucia et al., 2006). Our result is, however, in agreement with previous studies on the in low- and high-density environments (Kuntschner et al., 2002; Thomas et al., 2005). These results suggest that, in all environments, elliptical galaxies form on similar timescales.

The often-found differences in low- and high-density environments between the age (Trager et al., 2000a; Poggianti et al., 2001; Kuntschner et al., 2002; Terlevich & Forbes, 2002; Caldwell et al., 2003; Proctor et al., 2004a; Thomas et al., 2005) and [Z/H] (Kuntschner et al., 2002; Thomas et al., 2005), with galaxies on average being Gyr younger and more metal-rich in lower-density environments, are not reproduced here. Although, given the size of our errors it is not surprising that we do not detect such a small difference. These results are usually found comparing truly isolated galaxies with cluster galaxies. As the galaxies in the cluster-outskirts sample are actually drawn from the outer regions of the clusters and the structures surrounding them (out to a projected radial distance of Mpc or ), it is possible that the contrast between the average densities of each environment is not sufficient to reveal any differences in the stellar populations, and that the change occurs at a lower density threshold (e.g. between isolated galaxies and those in groups/filaments).

Figure 7: The trend of mean age (top), mean [Z/H] (middle), and mean (bottom) as a function of cluster virial radius. The mean is calculated in bins containing 15 galaxies.

Figure 7 shows the variations of the SPPs with projected cluster-centric distance, normalised to the cluster virial radius (). The lines in these plots show the mean values in bins containing 15 galaxies extending out to almost . The error bars show the standard error of the mean within each bin. We find no evidence of any significant trends, although it does appear as if and age increase moving towards the centre of the cluster, implying that the galaxies in the cluster cores are older and have shorter star-formation timescales than those in the cluster outskirts. Despite the lack of clear trends there are two other interesting aspects of these plots. Firstly, there appears to be a decrease in [Z/H] outside . Secondly, at a distance slightly less than the cluster virial radius there appears to be a dip in the average age. Such a dip would be expected in a scenario where interaction with the ICM triggers star formation in an in-falling galaxy, resulting in a stellar population characterised by a young age and extended star-formation timescale. This decrease in age begins at a radius suggesting that the influence of the cluster extends to large distances. We also note that all galaxies with ages Gyr are located near and the age of the youngest stellar population at a given radius increases moving towards the cluster core.

5 The Parameter– Relations

5.1 The cluster relations

Figure 8: The variations of the SPPs (left panel), [Z/H] (middle panel) and (right panel) with of the galaxies in the cluster sample. All three parameters are moderately correlated with . The red line in each panel is the linear fit to the data.

The variations of the SPPs with velocity dispersion are shown in Figure 8. All parameters are found to be moderately correlated with a high level of significance; for and for [Z/H] and . Performing linear fits to the relations we find

(2)
(3)
(4)

These fits are shown as red lines in Figure 8. While these results confirm the existence of the [Z/H]– and relations, the correlation of age with velocity dispersion found here is not so well accepted (see Section 1 for references).

The behaviour of age and with velocity dispersion is reminiscent of down-sizing (Cowie et al., 1996), where the typical mass of a star-forming galaxy increases with redshift. Looking at the distribution of ages, we see that at all velocity dispersions there exist galaxies with very old stellar populations, but the age of the youngest galaxy at a given velocity dispersion increases with velocity dispersion. The peak epoch of star formation in more massive galaxies thus occurred at higher redshifts.

Reference [Z/H]
Zero-point Slope Zero-point Slope Zero-point Slope
This study
        Cluster . 630.26 . 640.12 . 630.17 . 400.08 . 170.13 0. 200.06
        Cluster-outskirts . 430.45 . 540.20 . 240.40 . 180.18 . 520.31 0. 330.14
Thomas et al. (2005) . 46 0. 24 . 06 . 55 . 42 0. 28
Nelan et al. (2005) 0. 590.13 . 530.08 0. 310.06
Bernardi et al. (2006) . 720.31 1. 15 . 640.01 . 38 . 540.01 . 32
Smith et al. (2006) 0. 720.14 . 370.08 0. 350.07

Graves et al. (2007)
0. 350.03 0. 790.05 0. 360.04
Smith et al. (2007) . 640.12 0. 380.09 0. 360.07
Thomas et al. (2010) . 110.05 . 470.02 . 340.04 . 650.02 . 550.02 0. 330.01
Table 5: Comparison of the SPP– relations from this study and the literature.

Assuming that the scatter about the relations is Gaussian we find that the intrinsic scatter in is dex, in [Z/H] is dex and in is . The uncertainty in these scatters were determined via Monte Carlo simulations. Considering the mean observational errors are 0.14, 0.08, and 0.08 dex, respectively, the tightness of these relations is remarkable, and shows that the velocity dispersion is an excellent indicator of the SPPs in early-type galaxies, with more massive galaxies being older, more metal-rich and having shorter star-formation timescales than less massive galaxies.

Table 5 lists the SPP– relations found in this work and in the literature. The literature estimates come from a sample of early-type galaxies in high-density environments (Thomas et al., 2005), a sample of red-sequence galaxies in low- clusters (Nelan et al., 2005), a sample of early-type galaxies in high-density environments from the SDSS (Bernardi et al., 2006), a sample of red-sequence galaxies in low- clusters (Smith et al., 2006), a sample of red-sequence galaxies drawn from the SDSS (Graves et al., 2007), a sample of galaxies from the Shapley supercluster with km s (Smith et al., 2007), and a sample of red sequence galaxies in all environments.

Overall, the slopes found here agree well with those found in the literature. The slope of our relation is consistent with most estimates in the literature except for that of Thomas et al. (2005), which is only a third as steep as ours, and that of Bernardi et al. (2006) who find a slope twice as steep. The existence of a correlation between age and velocity dispersion is still being debated and this is reflected in the large variation in slopes found in the literature. A possible cause for this is the difficulty in accurately determining ages with the current set of models. The slope of our [Z/H]– relation agrees well with those found in the literature, with exceptions of Graves et al. (2007) and Thomas et al. (2010) who find a slope twice and 50 percent as steep, respectively. The slope of our relation is consistent with all of the literature values despite being the smallest.

5.2 The relations in the cluster-outskirts sample

The median values of the SPPs were found to be the same in both the cluster sample and the cluster-outskirts sample, as were the SPP distributions. In order to make a true comparison, one that is free from any biases introduced by the two velocity dispersion distributions, we now compare the parameter– relations found in the cluster sample with those in the cluster-outskirts sample.

Figure 9 shows the parameter– relations for the galaxies in the cluster-outskirts sample (solid red lines) compared with those in the cluster sample (dashed black lines). Details of the fits are given in Table 5.

Figure 9: The parameter– relations for the cluster-outskirts sample. The solid red lines are the linear fits to the cluster-outskirts sample and the dashed black lines are the linear fits to the cluster sample.
Figure 10: Comparison of the age (left), [Z/H] (middle), and [/Fe] (right) estimates obtained from using the restricted and unrestricted set of indices. The solid lines represent the 1-to-1 relation (see the text for details).

None of the SPPs are found to be significantly correlated with velocity dispersion in the cluster-outskirts sample. Note that the parameter errors are larger in the cluster-outskirts sample than the cluster sample. This is due to the fact that the galaxies in the cluster outskirts were observed with 6dF, which has less wavelength coverage than 2dF, and therefore their SPPs were estimated, on average, from fewer indices. It is possible that these larger errors blur any correlation that may exist.

It is also possible that the change in the number and combination of indices used to estimate the SPPs in the cluster-outskirts sample, when compared to the cluster sample, is the reason why no correlations are found in the former. We therefore check this effect by re-estimating the SPPs of the cluster sample using only , Mgb and Fe5335. Using these estimates we find that all three parameters are still correlated with velocity dispersion and that the slopes of both relations are consistent within the errors. Therefore it is unlikely that the lack of correlations in the cluster-outskirts sample is a result of the change in the number of indices used. We would like to point out that a fit (using the unrestricted set of indices) was only accepted if was used and at least two other indices. See Paper I for more details.

We show the results of comparing the two sets of estimates in Figure 10. For [Z/H] and the agreement between the two sets of estimates is quite good, although there is an offset of 0.05 dex in in the sense that the unrestricted set of indices gives larger values of . There is also an offset of 1.3 Gyr between the two age estimates (but in the opposite sense to that of the offset) and there is some scatter that increases with age. This is due to the fact that, in index space, the distance between lines of constant age decreases with increasing age so that small shifts in index strengths can lead to large changes in age estimates. According to a Spearman rank correlation test the two datasets are consistent. This implies that the two ways of measuring the stellar population parameters rank the objects in the same order and that there should be no effect on our results.

6 The Scatter in the Parameter Distributions in Clusters

In part, the spread in the SPP distributions found for the cluster sample is due to a combination of our observational errors and the correlations with velocity dispersion. To determine the amount of intrinsic scatter in the distributions, over and above that caused by the observational errors, we ran a series of numerical simulations. The method used was as follows.

Due to the need to create a large number of models containing a large number of galaxies, which need to have their SPPs converted to line-strengths (and vice versa), it is not feasible to estimate SPPs using all available indices. Therefore, for this exercise, we rely on the three indices used earlier in investigating the anti-correlation between age and [Z/H], i.e. , Mgb and Fe5335.

With this combination of indices, galaxies in the cluster sample have an age distribution that is approximately exponential and [Z/H] and have distributions that are approximately Gaussian (see Figure 5). Therefore, we began by selecting a range of -foldings for the exponential age distribution (, 0.15, 0.30, 0.55, 0.90, 1.60, 2.80, 5.00, 8.50, 15.00 Gyr), and ranges of Gaussian scatters in [Z/H] (, 0.05, 0.08, 0.12, 0.20, 0.30, 0.50, 0.80, 1.25, 2.00 dex), and (, 0.04, 0.07, 0.10, 0.15, 0.20, 0.30, 0.45, 0.70, 1.00 dex). Each range was chosen to be approximately evenly spaced logarithmically so as to have better resolution at small values. The medians of the cluster [Z/H] and distributions were used as the means of their Gaussian distributions, and the exponential age distribution was truncated at 5 Gyr (because the models are less reliable at young ages) and at 14 Gyr (the age of the universe).

A model was generated for each combination of , , and consisting of 10,000 mock galaxies with ages, [Z/H], and (parameter triples) drawn randomly from the specified distributions. If any of the mock galaxies had a [Z/H] or that fell outside the extent of the models111The Thomas et al. (2003) models have Gyr, dex, and dex. then they were assigned the closest value from the models; this was not necessary for the ages since they were truncated at the values stated above.

These parameter triples were converted, via the Thomas et al. models, to the corresponding , Mgb, and Fe5335 index values (index triples). This was achieved as follows. The models were divided up into cells defined by two adjacent values of each SPP, and for each mock galaxy the cell in which it fell was determined. Each cell is also defined by eight values of , Mgb, and Fe5335, corresponding to their values at the eight vertices of the cubical cell. The index triple corresponding to the parameter triple is then calculated by taking the mean of each of these eight index values weighted by the distance in parameter space of the mock galaxy from each corner of the cell.

These index triples were then perturbed by randomly drawing errors from an observed galaxy’s index error distributions. In doing this we cycled through the observed galaxies so that each observed galaxy had an approximately equal number of mock galaxies perturbed by its index error distributions. The perturbed index triples were converted back to parameter triples.

To ascertain how well the models fit the data a likelihood statistic was used. The SPP space was divided up into bins and the probability of each bin containing a galaxy was calculated. The age bins were 0.5 Gyr in width and ranged from 0 and 15 Gyr, the [Z/H] bins were 0.125 dex in width and ranged from to 0.7125 dex, and the bins were 0.025 dex in width and ranged from 0.0 to 0.5 dex. This resulted in 30 age bins, 24 [Z/H] bins, and 20 bins. Before the likelihood statistic was calculated, the model was lightly smoothed to minimise the number of bins with zero probabilities; a 3D Gaussian, with bins for all dimensions, was used as the smoothing kernel, and bins within 3, in each dimension, were used in calculating the value of the bin probability in the smoothed model (i.e. two bins either side in each dimension were used). The likelihood statistic is obtained by determining which bins the observed galaxies lie in and summing the logarithm of the bin probabilities.

Monte Carlo simulations were used to estimate the probability of obtaining a likelihood statistic larger than the observed one by chance. There are 103 galaxies with measurements of the indices required to estimate the SPPs in the cluster sample, so we simulate 103 galaxies in an identical manner to the model and calculate the maximum likelihood statistic. This is done 10,000 times. The fraction of simulations with likelihood statistics larger than the observed value are recorded and 3D confidence contours are generated.

Figure 11: Two views of the 3D confidence contours of the -folding of the exponential distribution of ages () and the RMS scatters in the Gaussian distributions of [Z/H] and [/Fe] ( and ), generated from the numerical simulations described in the text. The blue, green, and red surfaces are the 1, 2, and 3 confidence contours.
Figure 12: Slices, parallel to the age-[Z/H] plane, through the 3D confidence contours shown in Figure 11. Blue is , green 1–2, orange 2–3, and red . The value of the [/Fe] scatter used to generate the model is shown at the top of each panel. The cross in the panel with marks the model that is most consistent with our data.

These 3D confidence contours are shown in Figure 11, which presents the likelihood of our dataset being represented by a model with the specified -folding of the exponential distribution of ages and specified RMS scatters in the Gaussian distributions of [Z/H] and . While Figure 11 provides an overall picture of the acceptable scatters in the SPPs, more detailed information can be revealed by taking slices through the 3D confidence contours. Figure 12 shows slices taken parallel to the age-[Z/H] plane at values of corresponding to those used in generating the models.

These simulations provide us with a great deal of information regarding the intrinsic scatter in each of the SPPs. Firstly, it is difficult to constrain the -folding of the exponential age distribution. This is due to small uncertainties in line-strengths translating to large changes in the age estimate combined with relatively large observational errors in the index. Although models with small values of -folding are not ruled out, we find that our data is most consistent with the model having Myr. Secondly, small scatters in [Z/H] ( dex) are strongly ruled out, as are large scatters ( dex). We find the model with dex is the most consistent with our data. Finally, large scatters in ( dex) are also strongly ruled out. Models with low scatters in are not ruled out, but we find that the most consistent model is that with dex. The model that gives the maximum likelihood (i.e.  Myr, dex, and dex) is marked by a cross in Figure 12.

Since the SPPs were found to be correlated with velocity dispersion, and since the galaxies in the cluster sample have a range of velocity dispersions, it is understandable that we should detect an intrinsic scatter in the SPP distributions. The degree to which the intrinsic scatter in the parameter distributions is attributable to trends with velocity dispersion can be estimated by comparing the scatter expected given the velocity dispersion distribution in the cluster and the intrinsic scatter about the parameter– relations.

We use the parameter– relations to convert the galaxies’ velocity dispersions into parameter values. The scatter in these values is then calculated; the intrinsic scatter about the relation (as found in Section 5.1) is then added in quadrature to the scatter due to the relation with velocity dispersion, and the result is compared to that obtained from the simulations described above. We do this only for [Z/H] and , which were found to have approximately Gaussian distributions.

The scatter expected in [Z/H] on this basis is 0.21 dex which is comparable to the intrinsic scatter of dex estimated above. The expected scatter in is 0.06 dex which is very close to the estimated intrinsic scatter dex. It appears then that the intrinsic scatter in both the [Z/H] and distributions can almost entirely be accounted for by the parameter– relation and the intrinsic scatter about it.

For [Z/H], the scatter due to the correlation is 0.16 dex while the intrinsic scatter about the relation is 0.13 dex; thus, most of the intrinsic scatter in the [Z/H] distribution comes from the correlation with velocity dispersion. For , the scatter due to the correlation is 0.03 dex while the intrinsic scatter about the relation is 0.05 dex; thus most of the intrinsic scatter in the distribution comes from the intrinsic scatter about the relation.

7 Discussion

The process by which galaxies form and the factors with the greatest influence on their evolution are unresolved issues. In models of galaxy formation based on hierarchical merging in a CDM universe (e.g. De Lucia et al., 2006) the merger history of an early-type galaxy can fall anywhere between two extremes: mergers could occur early-on and rapidly with subsequent passive evolution—the revised monolithic collapse scenario (e.g. Merlin & Chiosi, 2006); or the galaxy could experience a more prolonged history of mergers—the extended merging scenario (e.g. Toomre, 1977). The environment of a galaxy and its mass are the two most influential factors on galaxy evolution but their effects need to be to disentangled to gain an insight into the relative importance of each.

For cluster galaxies, the numerical simulations performed here show that the intrinsic scatters in [Z/H] and , and the -folding of the exponential distribution of ages, are all quite small, as would be expected from a rapid formation at high redshift followed by passive evolution. Additionally, positive correlations are found between all three of the SPPs and velocity dispersion. The correlations found for both [Z/H] and confirm well-known trends (Trager et al., 2000a; Kuntschner et al., 2001; Proctor & Sansom, 2002; Thomas et al., 2002; Caldwell et al., 2003; Mehlert et al., 2003; Nelan et al., 2005; Thomas et al., 2005; Bernardi et al., 2006; Gallazzi et al., 2006; Kelson et al., 2006; Sánchez-Blázquez et al., 2006; Thomas et al., 2010). However the correlation found for age is not widely recognised; some authors find age and velocity dispersion to be positively correlated (Proctor & Sansom, 2002; Proctor et al., 2004a; Proctor et al., 2004b; Nelan et al., 2005; Thomas et al., 2005; Gallazzi et al., 2006; Bernardi et al., 2006; Thomas et al., 2010) while others find they are not correlated at all (Trager et al., 2000a; Kuntschner et al., 2001; Terlevich & Forbes, 2002). Not only do we find that age is positively correlated, but also that it is the most significantly correlated out of the three SPPs, being significant at the level. These correlations are qualitatively consistent with more recent semi-analytic models (De Lucia et al., 2006). These models incorporate feedback from AGN (Croton et al., 2006), which heats the available gas, preventing further star formation in massive galaxies and bringing the predicted scaling relations into agreement with those observed.

There is a level of homogeneity to early-type cluster galaxies evidenced in the similarity of their line-strength and SPP distributions and the consistency of the correlations between these quantities and velocity dispersion that is found between the clusters studied here. That this homogeneity is maintained amongst clusters of varying richness and morphology indicates that differences in the cluster environment have relatively little effect on the stellar populations of early-type galaxies. The dominant factor appears to be mass.

While mass plays a large role in determining the SPPs in early-type galaxies, it does not do so completely. The size of the role played varies; while [Z/H] is almost entirely a function of velocity dispersion, is less so. The intrinsic scatters in [Z/H] and in the cluster galaxies were found to be almost entirely accounted for by the scatter produced by the correlations with velocity dispersion and the intrinsic scatter about these relations.

Galaxies in low-density environments are observed to be, on average, Gyr younger than galaxies in clusters (Trager et al., 2000a; Poggianti et al., 2001; Kuntschner et al., 2002; Terlevich & Forbes, 2002; Caldwell et al., 2003; Proctor et al., 2004b; Denicoló et al., 2005; Thomas et al., 2005; Bernardi et al., 2006; Sánchez-Blázquez et al., 2006). The situation is not so clear with regards to differences in [Z/H] and . Recent models predict that galaxies in denser environments are older and more metal-rich than isolated galaxies (De Lucia et al., 2006). We do not find significant differences in the line-strength distributions or the SPP distributions between the cluster-outskirts sample and the cluster sample. However, the size of our SPP errors make it difficult to detect the small differences in age reported by other authors and any difference may be masked by the 1.3 Gyr offset to older ages found for galaxies that their parameters estimated from fewer indices; such galaxies are found predominantly in the cluster-outskirts sample. We do find that the tight correlations with velocity dispersion of both the line-strengths and SPPs that are found in clusters are weaker in the cluster outskirts, suggesting that the modes of formation in the cluster outskirts are more varied than those in the cluster cores.

Similar results were found by Thomas et al. (2010) who conclude that the formation and evolution of early-type galaxies are relatively insensitive to environment and are instead driven by self-regulation processes and their intrinsic properties such as mass. However, our result that the SPP trends with velocity dispersion are weaker in the cluster-outskirts than in the clusters is in conflict with these results (see also Bernardi et al., 1998, 2006). The dip in ages found near the cluster virial radius (see Figure 7) suggests that movement into the cluster environment may induce a burst of star formation and, combined with the down-sizing evident in Figure 8, that this burst may occur preferentially in lower mass galaxies (similar to the rejuvenated population from Thomas et al.). Presumably, our two samples (cluster and cluster-outskirts) are combined in their single high-density sample, which may result in the masking of this trend. Our results are broadly consistent with the results of Smith et al. (2006) who find a variation of the SPPs with cluster radius. Thomas et al. find that environment becomes more of an influence moving to less massive galaxies (see also Haines et al., 2006).

Our results can be best explained by the revised monolithic collapse model, but is also consistent with the extended merging model if the mergers are dissipationless (see De Lucia et al., 2006). Pipino et al. (2009) have a model of elliptical galaxy formation that implements a detailed treatment of chemical evolution, and they find that the correlation between and velocity dispersion is much less steep than that observed. Pipino et al. find that AGN quenching can help to improve the agreement, but this worsens their mass-metallicity relation compared to observations. They suggest that both relations can be reproduced provided the formation of all spheroids happens quasi-monolithically, i.e. the formation of the stars occurs in sub-units and that this star formation and the assembly of the sub-units into an elliptical galaxy occur at the same time and in the same place.

The star-formation rates in galaxies are found to increase with increasing distance from the cluster centre, and to converge to the mean field rate at distances greater than times the virial radius (Lewis et al., 2002, see also Gómez et al. (2003)). We find evidence that there is a dip in the mean ages of galaxies just inside the cluster virial radius, possibly due to secondary star formation that reduces the luminosity-weighted mean age. This could be evidence that in-falling galaxies, upon reaching the virial radius of a cluster, undergo a burst of star formation triggered by the dense intra-cluster medium. If such a burst only amounted to a small fraction of the galaxy’s total mass then its effect on the integrated light would be short-lived and the galaxy would rapidly return to appearing old and red. Similar to the findings of Lewis et al., we find that this decrease in age actually begins at , suggesting that the influence of the cluster environment extends to large distances. Whereas the result of Lewis et al. was based mainly on late-type galaxies, the remarkable thing about this result is that it applies to early-type galaxies.

There are two sources of bias that we must check have not influenced the above results: the number of indices used to derive the SPPs and and the aperture corrections. It is possible that the lack of correlations with velocity dispersion for the SPPs in the cluster-outskirts sample is due to the fact that, on average, fewer indices were used to estimate them than those in the cluster sample. This results in larger SPP errors and might potentially explain the lack of correlations with velocity dispersion. However, as we show in Section 5.2, using only three indices to estimate the SPPs does not significantly alter their distributions compared to those derived from an unrestricted set of indices.

It is also possible that mass segregation within the cluster could cause the weakening of the line-strengths in the cluster outskirts, if that is where less massive galaxies are preferentially found. This is a result of the same aperture correction being applied to a galaxy irrespective of how massive it is and despite the fact that the line-strengths being corrected were measured within differing effective radii. We find that our two samples (cluster and cluster-outskirts) have a similar shape to their magnitude distributions but that the galaxies in the cluster-outskirts are on average  mag brighter, due to the facts that there are more galaxies in the cluster sample and that we target the brightest galaxies. So the correlation of weak line-strengths for less massive galaxies cannot be the reason for the weakening of the trends with velocity dispersion in the cluster-outskirts galaxies. We see no reason, therefore, not to believe that the weakening of the relations in the cluster-outskirts is real.

The overall picture that emerges from this study is as follows. Early-type galaxies in clusters form a homogeneous class of objects that form in a process similar to a revised monolithic collapse and whose stellar populations are largely determined by their velocity dispersion (mass) and are relatively unaffected (at least differentially) by the cluster environment. The more massive they are the older and more metal-rich they are, and the shorter their star-formation timescales. The stellar populations of early-type galaxies in the outskirts of clusters, in contrast, appear less influenced by mass because, due to the varying environments they formed and evolved in, their evolutionary histories are more varied and this causes the correlations with mass to be less significant. A galaxy, especially a less massive one, that is falling into a cluster will, upon nearing the virial radius, undergo a burst of star formation. Once these stars have faded and ceased dominating the integrated light the galaxy will appear indistinguishable from those in the cluster core.

8 Summary

In summary, we have measured velocity dispersions, redshifts and absorption-line strengths for a magnitude-limited () sample of galaxies drawn from four clusters (Coma, A1139, A3558, and A930 at ) and their surrounds (extending to ). Using the fully-calibrated absorption-line indices coupled with the stellar population models of Thomas et al. (2003), we have estimated ages, [Z/H], and for 219 galaxies. We have used these data to investigate the effects of mass and environment on the stellar populations of early-type galaxies and our results can be summarised as follows.

  1. For galaxies in the cluster sample, all indices are positively correlated with velocity dispersion, with the exceptions of and , which are negatively correlated, and Fe5406, which is uncorrelated.

  2. Only Mgb and are correlated with velocity dispersion in the cluster-outskirts sample. The slopes of these two relations are consistent with those found for the cluster sample.

  3. The cluster cores are relatively free from young galaxies and from galaxies that have experienced recent star formation. These galaxies are more commonly found outside .

  4. The stellar populations in clusters form a homogeneous population. Despite the fact that our sample was drawn from four clusters spanning the ranges of Bautz-Morgan classifications and Abell richness classes, the line-strength– relations, parameter- relations, and SPP distributions are consistent between clusters.

  5. There is no difference between the line-strength distributions and SPP distributions in the clusters and their outskirts.

  6. The SPPs in clusters are correlated with velocity dispersion, suggesting that more massive galaxies are older, have shorter star-formation timescales, and are more metal-rich. These correlations are found to be weaker in the cluster outskirts.

  7. For galaxies in the cluster sample, the -folding time of the age distribution is 900 Myr, the intrinsic scatter in the [Z/H] distribution is 0.3 dex, and the intrinsic scatter in the distribution is 0.07 dex. These latter two intrinsic scatters can almost entirely be accounted for by the correlations with velocity dispersion and the scatter about the relations. We conclude, therefore, that the mass of a galaxy plays a major role in determining its stellar populations.

Further high quality observations of galaxies at higher redshifts will allow the development of a consistent model of early-type galaxy formation at all masses and in all environments.

The authors thank the anonymous referee for a careful reading of the paper and for the many helpful suggestions that improved it considerably.

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