THE 10k zCOSMOS: MORPHOLOGICAL TRANSFORMATION OF GALAXIES IN THE GROUP ENVIRONMENT SINCE z ∼1^*

COSMOS (Scoville et al. 2007a) is a multi-wavelength survey of a 2 deg² equatorial field, observed so far by the major earth- and space-based facilities, e.g., the Hubble Space Telescope (HST), Spitzer, the Galaxy Evolution Explorer (GALEX), Chandra, Subaru. zCOSMOS (Lilly et al. 2007) is a spectroscopic redshift survey in this field carried out with the VIMOS spectrograph on the ESO UT3 8-m VLT. The zCOSMOS-bright part of the survey is flux limited at I_AB < 22.5, and will ultimately obtain over 20,000 spectra. At this flux limit, the redshifts of the majority of the observed galaxies fall in the range 0 < z < 1.4. A higher redshift range, 1.4 < z < 3 is targeted in the zCOSMOS-deep program. Here, we use the first 10,000 spectra from zCOSMOS-bright, which we refer to as the "10k sample" (Lilly et al. 2009). The high-quality photometry in the COSMOS field also allows us to derive accurate photometric redshifts, with an uncertainty of 0.023(1 + z) or better. These are used to understand the spectroscopic completeness of the survey (see Lilly et al. 2009).

The rest-frame absolute magnitudes of all I_AB < 22.5 targets are measured using the spectral energy distribution (SED) fitting employing the ZEBRA code (Feldmann et al. 2006). The magnitudes are obtained as the best fit normalized to each galaxy photometry (Capak et al. 2007b) at the best available redshift, spectroscopic or photometric (P. Oesch et al. 2010, in preparation, see also Zucca et al. 2009). Stellar masses M_* are obtained from fitting stellar population synthesis models to the SED of the observed magnitudes as described in Bolzonella et al. (2009) and Pozzetti et al. (2009), using the best available redshift. The stellar masses that we use are obtained with the Bruzual & Charlot (2003) libraries and the Chabrier initial mass function (Chabrier 2003), the Calzetti et al. (2000) extinction law with 0 < A_V < 3, and solar metallicities. The assumed star formation history (SFH) is decreasing exponentially with a timescale τ, taking values from the interval 0.1 < τ < 30 Gyr. The stellar mass is obtained by integrating the SFH over the galaxy age, from which the mass of gas processed by stars and returned to the interstellar medium during their evolution ("return fraction") has been subtracted. See Bolzonella et al. (2009) for more details.

The detailed description of our group-finding algorithm and the group catalog are presented in Knobel et al. (2009). Here, we outline only the most important points regarding the group catalog.

Knobel et al. (2009) combine two standard group searching algorithms: friends-of-friends (FoF) and the Voronoi–Delaunay method (VDM) to define groups in the 10k zCOSMOS. The group-finding parameters are optimized based on tests of the COSMOS mock catalogs (Kitzbichler & White 2007) designed to match the geometrical and sampling properties of the 10k zCOSMOS catalog. Knobel et al. (2009) also developed a new "multi-pass" strategy that optimizes group finding over a range of richnesses by first optimizing for the largest groups and then subsequently moving down to groups with a smaller number of observed members.

The group catalog that we use in this work is the so-called "one-way-matched" catalog, which is the intersection of the independently created FoF and VDM catalogs. In total, there are 800 groups with at least two members in the current 10k sample. Over 100 of these groups have at least 5 spectroscopically observed members.

Extensive comparisons with the mock catalogs (Kitzbichler & White 2007) have established that the zCOSMOS 10k group catalog has a relatively high purity and completeness—82% and 81%, respectively, for groups with N ⩾ 5, and only marginally lower for the poorer groups. It should, however, be appreciated that these numbers are based on comparisons with the ideal group catalogs that could have been constructed (with two or more spectroscopic members per group) from a sparsely sampled "10k-like" dataset, rather than the actual set of all groups in the COSMOS volume. As a result, some of the galaxies that are not currently placed in a group are nevertheless likely to be in a group which will be identified in the future with higher sampling of the full survey. The current "non-group" sample will therefore contain some "group" galaxies, and this contamination will act to reduce observed differences between group and non-group populations. Partly for this reason, as discussed below, we will usually use the entire galaxy population that we have observed spectroscopically, selected without regard to environment, as our control sample. This also reflects the traditional definition of a "field sample."

Due to the non-uniform sampling scheme of the current 10k zCOSMOS survey (Lilly et al. 2007, 2009), the fraction of group members observed (as well as the chance of recognizing the poorer groups) will be a function of positions on the sky. We therefore correct the observed number of members for each group by the overall sampling fraction of the survey at that location, taking into account both the spatially variable spectroscopic sampling rate and the redshift-dependent success rate in yielding a high confidence redshift (using the corrections derived in Knobel et al. 2009, Equation (23)). We will refer to this as the corrected richness. Using the mock catalogs, Knobel et al. (2009) find that the corrected richness shows a relatively tight correlation with the estimated halo mass (see Figure 13 in Knobel et al. 2009) starting from groups with only two spectroscopically confirmed members. However, it should be noted that such defined corrected richness of the group overestimates the true number of group members by about 50%–100% on average (when using the M_B < −20 − z members), depending on the number of observed members (Knobel et al. 2009). Therefore, the corrected richness of a group should not be interpreted as a true number of members, but instead, it should be understood as an overall property of a group of any size, well correlated with its halo mass.

For any given physical group, this corrected richness will vary with redshift due to the changing luminosity limit that is associated with the observed I-band limit. We can deal with this by considering groups with a given corrected richness above some fixed luminosity limit, allowing this limit to evolve with redshift to account for the luminosity evolution of individual galaxies as best we can. We refer to such a set of groups as a "volume-limited" sample in that it should contain all groups of a given type, but this sample could still be potentially affected by the so-called progenitor bias since infall of new members will produce new groups in this volume-limited sample at later epochs. Moreover, given that the original group catalog is generated from a flux limited sample, there will be a slight bias with redshift because poor groups are more difficult to detect at high z than at low z. However, the distribution of corrected richness with redshift is rather flat, reassuring us that this effect is minor.

The distribution of corrected richnesses using the luminosity limit M_B < −20.5 − z in 0.1 < z < 1 is shown in the left panel in Figure 1. The corrected richness for the majority of the 10k zCOSMOS groups was measured using the members above M_B < −20.5 − z less than 10.

Zoom In Zoom Out Reset image size

For groups with N ⩾ 5, Knobel et al. (2009) provide the measure of the observed velocity dispersion. Moreover, Knobel et al. (2009) also give an estimate of the virial mass of the dark matter (DM) halo for all of the groups by assigning a halo mass to each group using the empirical relation between the halo mass and the corrected observed richness, calibrated at each redshift on the mock catalogs (Kitzbichler & White 2007). The distribution of these estimated halo masses for the zCOSMOS groups with corrected richness of at least two members with M_B < −20.5 − z detected in 0.1 < z < 1 is shown in the right panel in Figure 1. The redshift distribution of the DM halo masses is also rather flat. The groups which we are using for the analysis typically have halo masses in the range 12 < log(M_DM/M_☉) < 14. This emphasizes that the zCOSMOS volume to z ∼ 1 does not contain rich clusters of galaxies.

In parallel, we measure the morphological mix of galaxies in a sample of isolated galaxies, to further highlight the possible environmental segregation of galaxy morphological types. For this purpose, we use the sample of isolated galaxies defined by Iovino et al. (2010) as follows. First, the Voronoi volume is estimated for each galaxy in the zCOSMOS flux limited I_AB < 22.5 sample in the area defined by 14957 < R.A. < 15041 and 176 < decl. < 268 in 0.1 < z < 1. These Voronoi volumes are normalized by the median Voronoi volume in Δz = 0.2 centered at each galaxy redshift, to correct for the changing mean intergalaxy separation with redshift. Galaxies with the normalized Voronoi volume within the highest quartile of these volumes are defined as the isolated galaxies. Moreover, galaxies with Voronoi volumes that are too large determined with respect to the normalized mean Voronoi volume (∼10% of the preliminary sample of isolated galaxies), most probably affected by the survey borders, and galaxies determined to be in groups (∼14% of the preliminary sample of isolated galaxies) are removed from the sample. Based on the I_AB < 22.5 mock catalogs, about 90% of the galaxies defined as isolated using the described procedure should be the single occupants of their halos.

Following an original practice, in this paper we refer to a "field" sample as being all galaxies selected without regard of environment. In comparisons of the various relations, the field sample will always be chosen to exactly match the selection of the group and isolated samples of galaxies with regard to all non-environmental parameters, e.g., luminosity, mass, type, redshift.

The COSMOS field is the largest contiguous field covered by HST Advanced Camera for Surveys (ACS) images. The HST observations (Koekemoer et al. 2007) were taken in the F814W filter. ACS imaging affords the possibility to derive robust structural parameters and to confidently morphologically classify all galaxies into "Hubble types" down to about 24 mag (and possibly deeper), well below the flux limit of zCOSMOS-bright.

Here we use the structural parameters and morphological classification based on the Zurich Estimator of Structural Types (ZEST) and presented in Scarlata et al. (2007). The ZEST classification scheme is based on a principal component analysis of five non-parametric diagnostics of galaxy structure: asymmetry A, concentration C, Gini coefficient G, the second-order moment of the brightest 20% of galaxy pixels M₂₀, and the ellipticity . The morphological classification is performed in the space of the first three eigenvectors, which contain most of the variance of the original non-parametric quantities. At each point in the three-dimensional eigenvector space, a morphological class is assigned based on inspection with the naked eye and the median Sérsic index of all the galaxies in that cell.

Galaxies are classified by ZEST into elliptical, disk, and irregular galaxies. The disk galaxies are further split in four bins, namely bulgeless, small-bulge, intermediate-bulge, and bulge-dominated disk galaxies.

In the following we consider all galaxies that are classified by ZEST as either "elliptical" or "bulge-dominated" systems, i.e., specifically ZEST Classes 1 and 2.0, as "early-type". All other ZEST types are collectively considered to be "late-type" galaxies. In terms of the conventional Hubble classification scheme, our division would probably be between Sa and Sb.

In zCOSMOS, the targets to be observed spectroscopically are selected independently of the galaxy properties, except for the requirement of 15.0 < I_AB < 22.5. The failure to assign a redshift to observed spectra may have several causes, some of which may depend directly or indirectly on the properties of the target galaxies. We therefore adopt a weighting scheme to correct for the objects observed spectroscopically which have insufficiently good redshifts to be included in the HCC 10k sample (including complete failures) taking into account only galaxy properties. We define a multidimensional space by the selection magnitude I_AB, the rest-frame (U − V)₀ color, morphological type, and redshift, relying on the values calculated using high quality photometric redshifts. For each galaxy, the multi-parameter space is sampled for galaxies of the same morphological class within an interval, centered on the galaxy in question, that is 0.25 mag in I_AB magnitude, 0.25 mag in the rest-frame (U − V)₀ color, and 0.1 in redshift. We then define the inverse weight w_i of each galaxy i in the HCC 10k sample as the fraction:

$$\begin{equation} w_i = \frac{N_{\rm{HCC}10\rm{k}}^i}{N_{10\rm{k}}^i}, \end{equation} \tag{ 1 }$$

where Nⁱ_HCC10k is the number of galaxies in the HCC 10k sample and Nⁱ_10k is the number of galaxies in the total 10k sample which are neighbors of the ith galaxy in the above defined manner in the multidimensional I_AB − (U − V)₀ − z_phot-morphology space. In those cases where a galaxy in the 10k sample could not be assigned any of the properties considered (I_AB, (U − V)₀, z_phot and morphology) the galaxy is excluded from the analysis. We can neglect these galaxies given that their exclusion is based on the absence of data and not directly on the properties of galaxies. Moreover, they constitute a negligible fraction (<4%) of the total sample. The final number of the group, field, and isolated galaxies is 1859, 5671, and 1147 in 0.1 < z < 1 and in the selected area (see above), respectively.

Having defined the inverse weights of the galaxies in the HCC 10k sample using Equation (1), the fraction of galaxies of a given morphological type within any given galaxy sample is straightforwardly computed from the HCC sample in terms of the sum of these individual weights. Specifically, the total number of galaxies of a given morphological type T (using the ZEST morphological classification) in a given sample of galaxies is calculated using

$$\begin{equation} N_{T}^K = \Sigma _k \frac{1}{w_k(T)}, \end{equation} \tag{ 2 }$$

and summing over all T type galaxies in the K-subsample of the HCC 10k sample. Similarly, the total (weighted) number of galaxies of any type can be calculated using

$$\begin{equation} N_{\rm{ALL}}^K = \Sigma _k \frac{1}{w_k} \end{equation} \tag{ 3 }$$

summing over all galaxies in the K-subsample of the HCC 10k sample. The fraction of galaxies of a given morphological type T is then straightforwardly given by

$$\begin{equation} f_{T}^K = \frac{N_{T}^K}{N_{\rm ALL}^K}. \end{equation} \tag{ 4 }$$

The index K refers to the sample in which the morphological fraction of galaxies is calculated and is defined by environment, as well as by luminosity or stellar mass. In considering sets of galaxies defined by luminosity or mass, we decided to only consider intervals in either quantity which is essentially complete over a given redshift range, i.e., not to attempt a V/V_max type correction for incompleteness.

Uncertainties in the observed fractions are estimated using a bootstrap resampling of the given subsample of galaxies, setting the error bars in the f^K_T as the standard deviation in the distribution of fractions resulting from 1000 Monte Carlo bootstrap realizations.

To study the dependence of morphological segregation of galaxies in groups on the luminosity of galaxies, it is useful to first define "luminosity-complete," i.e., "volume-limited," samples of galaxies. We do this primarily to compare with the results in the literature, before turning to mass-selected samples below.

We define four galaxy samples which satisfy the following criteria: M_B < −19 − z at 0.1 < z < 0.5, M_B < −19.5 − z at 0.1 < z < 0.7, M_B < −20 − z at 0.1 < z < 0.9, and M_B < −20.5 − z at 0.1 < z < 1. We chose to use the (rest-frame) M_B magnitude because it is well matched to the observed I-band selection of zCOSMOS-bright at high redshifts, with an exact match at z ∼ 0.8, thereby assuring that the completeness of the zCOSMOS galaxies is not color dependent (see Iovino et al. 2010). At best, the "−z" term approximately accounts for the luminosity evolution of individual galaxies ΔM_B = −1 × Δz (see Kovač et al. 2010 for discussion). The number of galaxies in the luminosity-complete samples is given in Table 1. As shown in Figure 2, these galaxy samples should be statistically complete.

Zoom In Zoom Out Reset image size

Correspondingly, for each of these luminosity-complete galaxy samples, we can also define a set of "luminosity-complete" groups that satisfy the group criteria, i.e., that their corrected richness is at least two above these same galaxy luminosity limits. These groups should also be "volume-limited" in a sense, although it is clear that the accretion of new members may lead to a change in the group population through the relevant redshift range.

For the sample of volume-limited groups it is true that some groups will contain only one galaxy with spectroscopic redshift above the adopted luminosity limit, but one needs to note that all of these groups have at least two spectroscopically confirmed members, and therefore they are all real entities (obviously, within the uncertainties of the group finding process). The reason for the use of all the groups with corrected richness of at least two without respect to the number of spectroscopically confirmed members above the given luminosity limit is in order to keep the number of galaxies statistically meaningful when split to bins in redshift, luminosity (or mass), and environment, and when using the unique evolving luminosity limit over the whole redshift range. We have carried out tests which assure us that the obtained results are not driven by how we select volume-limited samples—i.e., with the two corrected or with the two spectroscopically confirmed members above the given luminosity limit.

With these considerations and caveats in mind, Figure 3 shows the fraction of early-type galaxies in different environments as a function of (evolving) absolute M_B magnitude. The black points show the field sample (all galaxies) while the green points show the set of isolated galaxies. The yellow points in each panel show the subset of galaxies that appear in the corresponding complete set of groups at that redshift, i.e., with more than two corrected members above a luminosity threshold for which we are complete, i.e., M_B < −19 − z for the 0.2 < z < 0.4 panel, M_B < −19.5 − z for the 0.4 < z < 0.6 panel, M_B < −20 − z for the 0.6 < z < 0.8 panel. The red points represent galaxies in groups with two or more members above M_B < −20.5 − z, for which we are complete across the whole redshift range. Apart from the caveats above about infall and progenitor bias, the group galaxies that are represented by the red points should therefore be directly comparable across the whole redshift range.

Zoom In Zoom Out Reset image size

It is clear from Figure 3 that the fraction of early-type galaxies is higher for brighter galaxies in all redshift bins, covering the range from z = 0.1 to z = 1. This reflects the strong and well-known dependence of morphology on mass or luminosity. In addition, however, the fraction of early-type galaxies at fixed M_B is higher for galaxies residing in groups compared with the overall population of field galaxies. This holds for every luminosity sample and at every redshift bin considered, even though the difference is sometimes within the margin of error. Similarly, the fractions of isolated galaxies with early-type morphologies tend to be lower than in the sample as a whole. In the highest redshift bin (0.8 < z < 1), the differentiation of the early-type fraction of galaxies in the different environments becomes negligible. Here, the morphological mix of early-type galaxies is within the errors the same in all environments.

Comparing the panels across the diagram, it is clear that the fraction of early-type galaxies at a given luminosity increases with time. This is more clearly seen in Figure 4, which shows the redshift/look-back time evolution of the fraction of early-type galaxies in three narrow ranges of M_B which are explored over three redshift intervals: 0.1 < z < 0.5, 0.1 < z < 0.9, and 0.2 < z < 1. As in Figure 3, the red points represent the members of a set of groups that is, in principle, volume limited up to z = 1, whereas the yellow points represent the members of a set of groups that is only volume limited within each individual panel. The redshift evolution of the early-type fraction seen in Figure 4 indicates a clear build-up over time of the population of luminous early-type galaxies in the group and field environments. For the isolated galaxies the build-up of early-type galaxies is detected only for the faintest galaxies. For the isolated galaxies with −21 − z < M_B < −20 − z the fraction of early types stays more or less constant since z = 0.9, but the error on the measured fraction at the lowest redshift is rather large and we do not have a sufficient number of isolated galaxies with −22 − z < M_B < −21 − z to reliably carry out this analysis.

Zoom In Zoom Out Reset image size

From Figure 3, it can be seen that the fraction of early-type galaxies in the group environment is higher than the fraction of early-type galaxies in the field (all galaxies), which is again higher than the early-type fraction in the isolated galaxies. By fitting a simple linear relation between the fraction of early-type galaxies and the look-back time, the data suggest that the morphological transformation of galaxies from late to early type has generally happened earlier for galaxies residing in groups than for galaxies of the same luminosity in the field, coupled with an overall trend for the transformation to occur earlier for more luminous galaxies. We will quantify this further below.

The evolution of the early-type fraction over cosmic time and its dependence on luminosity qualitatively mirrors (i.e., it is inverse to) the evolution and its environmental and luminosity dependences of the fraction of blue galaxies in the zCOSMOS group, field and isolated samples, investigated by Iovino et al. (2010).

4.1.1. Comparison with Literature

In the previous section we have seen the changes in the morphological mix of galaxies in groups over cosmic time. Comparison of the yellow and red points in the panels on the left sides of Figures 3 and 4 also suggests a dependence on the group properties, since the yellow points represent groups that extend to poorer levels than the red points, which represent galaxies in (rich) groups that have at least two members above M_B < −20.5 − z. Desai et al. (2007) have shown that morphological evolution of galaxies at z < 1 is stronger in lower mass clusters than in the most massive ones and there have been number of claims that the strongest evolution between z ∼ 1 and z ∼ 0 in the galaxy properties has been in the intermediate mass (e.g., Poggianti et al. 2006) or density (e.g., Smith et al. 2005) environments.

We can use the group corrected richness and measured velocity dispersion to study the morphological segregation as a function of a group property in our own sample. While the best way to isolate the effect of a group property would be to use galaxies in a narrow range of physical properties selected in a narrow bin of group properties, that type of analysis is not possible with the current 10k zCOSMOS sample due to the small number statistics. Therefore, we use instead the luminosity-complete samples of galaxies in groups of similar properties.

4.2.1. Group Richness

First, we look at the dependence of the morphological fraction of galaxies as a function of the corrected richness of the host group. We carry out this study for the four luminosity-complete samples defined above, using the group corrected richness defined in each of the luminosity-complete samples, i.e., the corrected number of members above the given galaxy luminosity limit. We split the group galaxies in bins using the corrected richness of a group (above the quoted luminosity limit) between 2 and 5, between 5 and 8 and larger than 8 for the groups in the luminosity-complete samples up to a luminosity of M_B < −20 − z. For the brightest sample M_B < −20.5 − z we define bins of group corrected richness between 2 and 7 and larger than 7, considering only galaxies and groups in 0.4 < z < 1 in order to keep the statistics meaningful. The results are shown in Figure 5. For lower luminosity galaxies, there is a clear trend for the richest groups to have a higher early-type fraction, especially as the redshift decreases.

Zoom In Zoom Out Reset image size

4.2.2. Velocity Dispersion

This analysis can be repeated using the observed velocity dispersion for the groups. Due to the large uncertainties related to velocity dispersion measurements (see Knobel et al. 2009), only groups with at least five observed members (above the I_AB < 22.5 cut) are used for this analysis. Using the four previously defined luminosity-complete samples of galaxies, we divide the groups into two sets according to their velocity dispersion: 250 < σ < 500 km s⁻¹ and σ>500 km s⁻¹. The fraction of early-type galaxies in these two group bins is shown in Figure 6.

Zoom In Zoom Out Reset image size

Even though this is of a lower significance, the same picture emerges as before. The fraction of early-type galaxies is larger in the groups with larger velocity dispersion for galaxies fainter than M_B = −19.5 − z. For brighter galaxies we do not detect any significant difference between fractions of early-type galaxies in groups of different velocity dispersion, possibly due to the limited number of galaxies.

For comparison with the literature, the above discussion was based on the rest-frame B-band luminosity. As well as the obvious sensitivity of the B-band luminosity to the recent star formation history, there are many reasons to prefer stellar mass as a yardstick of galaxy properties. In particular, as mentioned in Section 1, the existence of a correlation between the stellar mass function of galaxies and their environment (Baldry et al. 2006; Bolzonella et al. 2009), plus the strong correlation between mass and galaxy properties, means that any sample that contains a significant range of masses may show a spurious environmental dependence simply because of the different distribution of masses in the different environments. This will be true not only for B-selected samples, but also K-selected samples, and even mass-limited samples (i.e., all galaxies with masses above some threshold). The spurious environmental effects produced by this difference in mass functions is shown by the clear flattening of the observed color–density and morphology–density relations (Cucciati et al. 2010; Tasca et al. 2009) when going from narrow M_B luminosity bins to narrow mass bins.

Using the overall zCOSMOS density field (Kovač et al. 2010), Bolzonella et al. (2009) have shown that the stellar mass functions of galaxies are different in different environments up to at least z ∼ 0.7, and probably at higher redshifts. The galaxy stellar mass function in the densest regions, defined by the highest quartile in the distribution of galaxy environments at that redshift bin, is of bimodal shape at least up to z ∼ 0.5, showing an upturn at low-mass end and with massive galaxies preferentially residing in these densest regions. Bolzonella et al. (2009) explain the environmental dependence of the shape of the stellar mass function by the different relative contributions of galaxies of different types in different environments. The individual stellar mass function for each of the different types is well represented by the Schechter function in all environments (see Figure 4 in Bolzonella et al. 2009). The higher contribution of the red/early objects in the densest environments produce a characteristic "bump" at high-mass end in the stellar mass function in the densest environment.

In this paper, we are investigating the morphological properties of galaxies in the group environment (Knobel et al. 2009), corresponding to virialized structures (i.e., single dark matter halos)—and can be confident from the comparison with the mocks that this is indeed to a large degree the case (Knobel et al. 2009). Not surprisingly, galaxies in the identified groups reside also in the denser environments (see Figure 22 in Kovač et al. 2010), and the groups are themselves good tracers of the dense peaks in the density field (see Figure 23 in Kovač et al. 2010). However, there is not a one-to-one correspondence between the group and the continuously defined environment.

We have therefore recalculated the stellar mass function for the samples of the group and isolated galaxies used in this paper, following exactly the same methodology as described in Bolzonella et al. (2009). The stellar mass functions are calculated using the 1/V_max method, by using the additional weights for each galaxy to correct for the average sampling and redshift success rate of the 10k HCC zCOSMOS sample to the full 40k sample (as the stellar mass function deals with the volume densities and not fractions of objects, similar to the weights used to define the group richness). The errors correspond to Poissonian errors obtained from the 1/V_max method. The V_max refer to the total zCOSMOS volume, and therefore the normalization of all stellar mass functions, except of the one of the total sample of galaxies, is arbitrary. As for the rest of the analysis in this paper, galaxies are selected to reside in the central zCOSMOS region, defined in Section 3.

The resulting stellar mass functions for the group and isolated sample of galaxies for four redshift bins are shown in the left and right panels in Figure 7, respectively (black symbols and curves). The mass functions are fitted with a double Schechter function (with a unique value of the exponential cut-off) in the two lower redshift bins and with a single Schechter function in the two higher redshift bins. To be able to compare similar group environments at different redshifts, we select only group galaxies residing in the groups with at least two corrected M_B < −20.5 − z members. The shape of the stellar mass functions in the sample of group and isolated galaxies is reminiscent of the shape of the stellar mass functions in the sample of galaxies in the highest and lowest quartile of overdensities in Bolzonella et al. (2009). For the group galaxies, similar results are obtained when using all group members without restriction in the group richness—smoothing slightly the characteristic bimodal shape of the mass function in the dense region in the two lowest redshift bins, as expected when including in the galaxy sample also members of the smaller groups.

Zoom In Zoom Out Reset image size

We also calculate stellar mass function per morphological type in different environments, using the morphological classification described in Section 2.5. As expected, the high mass end of the stellar mass function in both environments is dominated by early-type galaxies, peaking at roughly 10¹¹ M_☉. Toward lower masses, the number of early-type galaxies decreases and the number of late-type galaxies increases. Late-type galaxies dominate below the crossing mass (the mass at which the two mass functions cross) and this crossing mass shifts toward lower values at later cosmic epochs. Since z ∼ 0.7, the crossing mass is clearly lower for the group than the isolated sample of galaxies. We will discuss the crossing mass in more detail in the following sections.

We therefore find that the stellar mass function exhibits a similar shape dependency on environment, whether environment is defined as a continuous field (density of objects) or a discrete (groups/isolated sample) quantity. Moreover, the reason is the same: the different relative contributions of galaxies of different types across a range of masses (see Bolzonella et al. 2009 for more discussion).

We stress that one consequence of this for any analysis related to the environment, is that whenever there is a sample of galaxies that contains a range of stellar masses, then the relationships between a given galaxy property and environment will be modulated by the relationship between that property and stellar mass through the differing mass distributions of galaxies with environment. To isolate the true environmental effect, we must consider galaxies in narrow stellar mass bins.

We therefore select four stellar mass-complete samples of galaxies to investigate the morphological mix inside and outside groups in zCOSMOS. The selection of the complete stellar mass samples has been described in Pozzetti et al. (2009), and is optimized to be complete for both early- and late-type galaxies following our definition of morphological types. We use the samples that are 85% complete for the early-type (1+2.0) galaxies. The samples are defined as follows: log(M_*/M_☉)>9.88 in 0.1 < z < 0.45, log(M_*/M_☉)>10.21 in 0.1 < z < 0.6, log(M_*/M_☉)>10.68 in 0.1 < z < 0.8, and log(M_*/M_☉)>10.96 in 0.2 < z < 0.95. The numbers of galaxies in the different environments within these mass-complete samples are given in Table 2.

The morphological mix of galaxies within these mass-selected samples in different environments is shown in Figure 8. The stellar mass bins have a width of Δlog(M_*/M_☉) = 0.7 (dictated by the number statistics), starting from the lowest stellar mass for which the samples will be complete. This means our mass bins are partially overlapping, and consequently, not independent of each other.

Zoom In Zoom Out Reset image size

For the stellar masses below ∼log(M_*/M_☉) = 11 we observe a steady increase with cosmic time in the fraction of early-type galaxies in all environments. For the highest mass bin, 10.96 < log(M_*/M_☉) < 11.66, the number of galaxies is small, and little can be conclusively said regarding the groups and for the field. However, it seems clear that high fractions ∼70%–80% of early-type ∼log(M_*/M_☉)>11 galaxies in both the group and field are present before z = 1 and that the morphological mix stays more or less constant since then.

Progressing to lower masses, we find that, at a given stellar mass, the fraction of early-type galaxies is consistently highest in the group environment, and lowest for the isolated galaxies, at every redshift that we can examine for that particular stellar mass. Fitting a linear relation between the early-type fraction and look-back time, the linear fits for galaxies with log(M_*/M_☉) ≲ 11 suggest that the fractions of early-type galaxies were more or less the same in all types of environment at higher redshifts and then, with cosmic time, diverged with progressive morphological transformation from late- to early-type galaxies happening at different rates in different environments at a given mass. As noted above, there is an indication that the increase in the early-type fraction over cosmic time is more rapid in the groups with higher richness than in the poorer groups (e.g., difference between red pentagons and yellow squares and the corresponding linear fits in Figure 8).

Looking at the same data from another perspective, we can calculate the fractions of early-type galaxies as a function of stellar mass in the narrow redshift bins: 0.2 < z < 0.4, 0.4 < z < 0.6 and 0.6 < z < 0.8. These are shown in Figure 9, using only groups with a corrected richness of at least two in the M_B < −20 − z sample, as we extend this analysis only to z = 0.8. At every redshift, the fraction of early-type galaxies increases strongly with the stellar mass for galaxies residing in both the groups and in the field. The isolated galaxies follow the same trend in the lowest redshift bins up to z = 0.6, while in the highest redshift bin they become very rare objects and the obtained statistics is much less reliable. This figure also illustrates the convergence of the morphological mix at a given (relatively high) mass at redshifts approaching z ∼ 1.

Zoom In Zoom Out Reset image size

These results are in good agreement with Tasca et al. (2009), who showed the weakening of the overall morphology–density relation at high stellar mass and/or high redshifts in similar mass-complete samples in the zCOSMOS. However, the increase of the early-type fraction with stellar mass in 0.2 < z < 0.8 (Figure 9) contrasts with results obtained by Holden et al. (2007), who do not detect any clear trend in the early-type fraction with stellar mass for the cluster galaxies more massive than log(M_*/M_☉) = 10.52. We have taken into account the difference in the initial mass function (IMF) used by Holden et al. (2007) and here, assuming that the stellar masses calculated with the Chabrier IMF are larger by 0.08 than the "diet Salpeter" IMF used by Holden et al. (2007; see, e.g., Bolzonella et al. 2009 on the differences between the stellar masses with different IMFs). Holden et al. (2007) results are obtained for five massive X-ray clusters in 0.023 < z < 0.83 spanning a range in velocity dispersion 865 km s⁻¹ < σ < 1156 km s⁻¹, or with 56 to 109 members above the quoted mass limit. The measured fractions of early-type galaxies are between 71% and 100%, comparable to the fractions we measure only for the most massive >log(M_*/M_☉) ∼ 11 galaxies. This indicates that clusters are either more efficient in transforming late-types to early-types or that the bulk of morphological transformation of galaxies more massive than log(M_*/M_☉) = 10.52 has happened earlier in the clusters than in any other environment, and specifically the poorer group environments examined here.

Figures 8 and 9 also show one way of looking at the relative importance of mass and environment in driving morphological transformation. It can be seen that the morphological mix that is achieved in the groups at some redshift and at some mass, is achieved at only slightly later times (or equivalently for slightly higher masses) in the field (all galaxies) and in the isolated galaxies. At z ∼ 0.5 and log(M_*/M_☉) ∼ 10.2, the "effect" of group environment is equivalent to only about 0.2 dex in stellar mass or to about 2 Gyr in time.

Fitting the linear relation to the observed f_early − log(M_*/M_☉) trends at a given redshift bin, we can calculate the stellar mass at which 50% of galaxies in a given sample is of early-type at that redshift. We call this quantity the morphological crossing mass since it is also obviously the mass at which the individual mass functions of the two populations cross. The change with redshift of the morphological crossing mass in the group and other environments is shown in Figure 10. The morphological crossing mass decreases with decreasing redshift, indicating that the morphological transformation from late to early-types starts in galaxies with higher stellar masses and shifts to galaxies with lower stellar masses over cosmic time. This is another manifestation of the so-called downsizing scenario in the evolution of galaxies (e.g., Cowie et al. 1996). At z ∼ 0.7 or a little above, 50% of galaxies with masses of log(M_*/M_☉) ≈ 10.85 are already of early-type, independent of their environment. Moving toward lower redshifts, the morphological crossing mass decreases more rapidly for galaxies residing in groups than for the field and isolated galaxies reflecting the emergence of morphological segregation.

Zoom In Zoom Out Reset image size

The above results have painted a consistent picture of a morphological segregation emerging between the typical group and field environments (i.e., all galaxies) emerging over the last several billion years, since z ∼ 1, and of being more prominent in galaxies of lower luminosity and/or stellar mass. Corresponding trends in the zCOSMOS 10k sample relative to the larger scale density field were shown in Tasca et al. (2009).

On the one hand, it is clear that this emerging environmental dependence is superposed on top of a global and strong mass-driven evolution that is seen in the whole population. There is no doubt that the stellar, or possibly total baryonic, mass ("nature") is directly related to the processes responsible for this morphological transformation. The offset between the observed fractions of different morphological types of galaxies in different environments since z ∼ 1, i.e., higher fractions of early-type galaxies for the group than the typical field population, which are again higher than the fractions for the isolated galaxies (Figure 8), is, however, tuned by the environment. As noted above, at a given mass, this environmental tuning corresponds to about 2 Gyr in time: a certain morphological mix, a product of the efficient morphological transformation, will be achieved first in the group, then in the field and at the end in the isolated environments for galaxies of a given mass.

However, it is not immediately clear if this is because of an offset in "starting time," as the more massive galaxies are expected to be formed first in the more massive structures (again "nature," e.g., Kauffmann 1995; Benson et al. 2001; Heavens et al. 2004), or because of a difference in the rate of evolution in different environments ("nurture"), caused by some of the dense environment related processes (e.g., ram pressure stripping, harassment, etc., see Section 1).

Moreover, we do clearly detect an apparent increase in the environmental differences, at least for lower mass galaxies which are transforming at lower redshifts. This produces the clear divergence of the morphological crossing masses from z ∼ 0.7 to z ∼ 0.3 in different environments, suggesting that the morphological transformation rate is rather faster in the groups than outside of them. However, an interpretation of Figure 10 in terms of the physically relevant processes is not trivial, since it also reflects both the shape of the mass functions and their relative amplitudes in different environments.

We therefore investigate the rates of the morphological transformation more directly. It is also of interest to compare the transformation rates for other relevant transformations, and specifically those related to the star formation history, i.e., the "quenching" transformation from blue to red, or from active star formation to passive evolution. Of course, all of these processes may be reversible, and so we are really looking at the "net" transformation rate. Comparison of these transformation rates may provide clues as to the physical linkage between morphological transformation and star formation quenching.

One interesting question regarding morphological transformation and star formation quenching is whether one preceded the other. Based on the field stellar mass functions of the zCOSMOS galaxies of different types, Pozzetti et al. (2009) find that the morphological crossing mass has higher values than the equivalently defined crossing mass for the populations of photometrically red and blue, and also active and passive galaxies. From the differences in the number density of photometrically and morphologically early-type galaxies, the inferred delay time between the color and morphological transformation is about 1–2 Gyr. A similar timescale is derived for the transformation to red colors after a switch in the star formation. Bundy et al. (2006) qualitatively find the same behavior for the crossing mass of the DEEP2 field galaxies when the population of galaxies is split according to the morphology and color, extending the color/morphology dichotomy of crossing mass to redshift 1.4.

Similar results have been obtained for the population of cluster galaxies. Wolf et al. (2009) study the population of galaxies in the A901/2 cluster complex at z ∼ 0.17, finding the majority of high mass galaxies (above 10¹¹ M_☉) to be red and spheroidal in all environments (outskirt, center, and outside of cluster). Based on the large number of cluster spirals in the mass range of 10¹⁰–10¹¹ M_☉, Wolf et al. (2009) conclude that quenching of star formation in these galaxies is a slow process, where the timescale of morphological evolution must be longer than that of the spectral evolution. However, at even lower masses, not accessible by our study, decline in star formation rate and morphological changes appear to be more synchronized in A901/2. Using the sample of 24 clusters from the EDisCS (White et al. 2005), Sánchez-Blázquez et al. (2009) find that the fraction of early-type red sequence galaxies decreases by ∼20% from z = 0.75 to z = 0.45, which can be expected if the cluster spiral galaxies first get redder, stopping their star formation, before they become early-type (note that Sánchez-Blázquez et al. 2009 have done the analysis using the luminosity-complete samples).

Using the marked correlation statistics on the Sloan Digital Sky Survey (SDSS) data, Skibba et al. (2009) conclude that z ∼ 0 red spirals are often satellites in the outskirts of groups and clusters, while red early-type galaxies are preferentially located in the centers of these structures. Skibba et al. (2009) suggest that the timescale of the morphological transformation of these red spirals is longer than that of the quenching of their star formation. The zCOSMOS extends a high-redshift (up to z ∼ 1) comparison between the color and morphological properties of galaxies to the group environment.

To enable a closer comparison between the color and morphological properties of galaxies in the group environment, we calculate the color crossing mass using the same procedure and the same galaxy samples that were used to calculate the morphological crossing mass, described in Section 4.4 (see also Iovino et al. 2010 who calculate a similar quantity, t_{50 − 50}, the cosmic time at which the fraction of red/blue galaxies is 50%). In addition, we also calculate the crossing mass for star formation activity by partitioning galaxies into active and passive classes using the specific star formation rate (sSFR) from the SED fitting (see discussion in Pozzetti et al. 2009 on the agreement between the star formation rates derived from these SEDs and those from measurement of emission lines). In this work, we consider galaxies with U − B > 1.1 to be red, and galaxies with log(sSFR/yr) < −10.5 to be passive. These crossing masses for the group and field samples are shown in Figure 11.

Zoom In Zoom Out Reset image size

The crossing mass for each of the samples shows behavior similar to what we have already shown for the morphological crossing mass. It shifts to lower masses with cosmic time in both the field and group environment, and since z ∼ 0.6, this evolution is clearly environment dependent. The activity crossing mass is systematically lower than the color crossing mass, which is systematically lower than the morphological crossing mass. This is observed both in the field (in agreement with Pozzetti et al. 2009) and in the group environment. Extrapolating the plot, at a given mass 50% of the population will turn passive at an earlier cosmic time than the time at which 50% of the population will become red. Fifty percent of the population will become early morphological type even later. Moreover, this will generally happen earlier for a group galaxy than for a field galaxy. A similar sequence of the color and morphological crossing mass in the zCOSMOS has been presented in Bolzonella et al. (2009) for the environments of extreme densities, when quantifying environment using the local overdensity of neighboring galaxies (Kovač et al. 2010). Bundy et al. (2006) find tentative evidence for the rise of the quiescent population in dense, continuously defined environments.

While the exact values of the crossing mass are strongly dependent on how galaxies were divided into types, there is a clear and progressive (with epoch) environmental dependence in these values. The effective transformation of galaxies from active to passive, from blue to red, and from late to early moves progressively toward lower mass galaxies as cosmic time passes or as the environment is denser. Derived values of the various crossing masses are consistent with a scenario in which, for the majority of galaxies, the timescale for the morphological transformation is longer than the timescale for the color transformation, both in the field and group environment, assuming that all these processes started to act approximately at the same time in a given environment.

Unfortunately, it is hard to use arguments such as the location and rate of change of the above-defined crossing mass to infer quantitative information on the transformation rates, since these may be sensitive to the choice of the location of the dividing line between the two properties and also on the shape and relative normalization of the mass functions of different components of the population. The dividing line may be clear for color (e.g., the so-called "green valley") but more arbitrary in the case of morphological classification. The relative amplitude of the mass functions of early- or late-type galaxies, and of blue or red galaxies, or of active or passive galaxies, will also change the location and movement of M_cross. Use of the redshift/epoch axis to determine transformation rates, i.e., of the flux of galaxies crossing through a chosen dividing line, is likely to be less sensitive to the precise location of that divide and to allow a more direct study of these questions.

In the following, we explore more directly the "transformation rate" of late-type galaxies into early-type galaxies for different masses and different environments in order to try to better understand the physical causes. It should be noted in the following discussion that this is really a "net" transformation rate from late to early, since it is in principle possible for early-type galaxies to reacquire a gaseous disk and become of later morphological type, although whether this would be sufficient to cross our defined morphological divide between ZEST classes 2.0 and 2.1 is unclear.

Assuming from now on that galaxy transformations are dominated by one-way transformation from late to early (and blue/active to red/passive), we proceed to define a normalized transformation rate η in which the rate of change in the number of "progenitor" galaxies (either late-type, blue, or active) is normalized by the number of these progenitors:

$$\begin{equation} \eta = - \frac{1}{N_C} \frac{dN_C}{dt} = - \frac{d \ln N_C}{dt}, \end{equation} \tag{ 5 }$$

where N_C is a measure of the number of progenitors of a given class C, i.e., the mean comoving density averaged over suitably large volumes of the universe.

The inverse of η gives the transformation timescale t_η for a typical "progenitor galaxy" to be transformed. The transformation rate η might be expected to be a function of mass, environment, and probably epoch.

Unfortunately, an accurate determination of N_C(z) and dN_C/dt for a particular class C of galaxies is observationally challenging. It requires an accurate measurement of galaxy properties, e.g., the stellar mass, over a range of redshifts, careful treatment of large-scale density variations within surveys due to large-scale structure, and, ideally, knowledge of the changes in the number of galaxies in a particular class due to, for instance, mass growth through star formation and/or merging. In the case of galaxies defined by environment, i.e., those in groups, there will also be a change in the population due to the hierarchical growth of the groups through the accretion of galaxies onto the virialized structures.

In cases where it can be assumed that the total number of galaxies in a given bin (defined by mass and environment) is more or less constant, then some of these difficulties can be alleviated by considering the fraction of galaxies, rather than their absolute number, i.e., by dividing by a fixed total number of galaxies N. In this case,

$$\begin{equation} \eta = - \frac{1}{f_C} \frac{df_C}{dt} = - \frac{d \ln f_C}{dt}. \end{equation} \tag{ 6 }$$

If the evolution of ln f_C is linear with cosmic time, we simply obtain η as the slope to this relation for any sample defined by mass and environment. With the limited baseline in redshift and limited number statistics, we will henceforth consider the rate η as single time-averaged rate over the accessible range of epochs, from a linear fit to ln f_C–t.

For group galaxies, we know that the total number of galaxies is certainly not conserved, because galaxies will be accreting onto the group from the surrounding regions. It is clear that this migration into the groups is likely to further amplify any environmental difference in transformation rates, because the new arrivals will have to "catch up" with the existing group members which already have a more evolved state.

In the following, we derive a simple first-order correction accounting for the galaxies infalling to the groups by assuming (1) that the total number of galaxies in the sample (at a given mass) is conserved, i.e., we do not consider galaxy mergers and neglect the effects of star formation, and (2) that the infalling galaxies can be considered to be a representative subset of the non-group population. This latter condition may not be true, and this infall correction is therefore likely to represent an upper bound to the actual transformation rate.

In some small increment of time dt, the number of class transformations dN in groups will be given by

$$\begin{equation} dN = -N_G df_{CG} - (f_{CG} - f_{CN}) dN_G \end{equation} \tag{ 7 }$$

where N_G is a number of the group galaxies, f_CG and f_CN are fractions of the C-class galaxies in the groups and non-groups, respectively, and where the class C is a "progenitor" type of galaxy (i.e., assumed to be late morphological type or active/blue type). The equation above can be further written as

$$\begin{equation} dN = -d(N_G f_{CG}) + f_{CN} dN_G. \end{equation} \tag{ 8 }$$

By normalizing the number of transformations with N_Gf_CG, which is the "pool" of potential objects in the group to be transformed, the rate η_IN,CORR including the effects of infall can be written as

$$\begin{equation} \eta _{\rm{IN,CORR}} = - \frac{1}{f_{CG}} \frac{df_{CG}}{dt} + \left(\frac{f_{CN}}{f_{CG}} - 1 \right) \frac{1}{f_{G}} \frac{df_G}{dt}. \end{equation} \tag{ 9 }$$

In the case of no infall, where f_G is constant over time, or in the case where the group and non-group populations have the same properties at a given epoch, it can be seen that the rate η will be given just with the first term on the left-hand side, which is the same as Equation (6) above.

What about progenitor bias? By considering two simple complementary categories, group and non-group, and the change in the fraction of galaxies associated with each, we automatically deal with both additional membership of pre-existing groups and the emergence of new groups where none previously existed (above the fixed threshold in richness). We should, however, recognize that the rates so derived will be averages across the entire, evolving, group population and not, necessarily, representative of what is happening within a single group. Because of the attraction of using two complementary populations, group and non-group, we no longer consider either the isolated galaxies nor the field (all galaxies) populations in this analysis.

It is important to note that, based on extensive comparisons with the mock catalogs, neither the completeness nor purity of the group catalog are believed to depend significantly on redshift (Knobel et al. 2009, see Figure 9). The same is also true of the individual group members. This allows us to use the observed fraction of galaxies in a volume-limited sample of groups as a good estimate of the infall rate from the non-group into the group population, and the observed morphological mix of galaxies in and outside of those groups as representative of both populations. The redshift evolution of the fraction of galaxies residing in the groups with at least two corrected members above M_B < −20.5 − z is shown in Figure 12. At a given stellar mass, the fraction of galaxies residing in the group environment increases markedly with cosmic time, building up these structures. At a given time, a larger fraction of the more massive galaxies are already present in the groups reflecting the different mass functions shown above (see Section 4.3 and Figure 7).

Zoom In Zoom Out Reset image size

The derived rates of the morphological transformation η_{L − >E} in the group environment are shown in the left-hand panel in Figure 13. We obtain the infall corrected rates taking for the term $\frac{f_{CN}}{f_{CG}}$ the average of the measured fractions at different times at a given mass, discussed in Section 4.4 (see Figure 8). The errors are obtained by the error propagation of Equations (6) and (9), using the individual bootstrap errors on the fractions. The red filled circles represent the rates corrected for infall using Equation (9), while the red open circles represent those computed directly from Equation (6), which are lower, as expected. The equivalently derived rates for the non-group galaxies, which are galaxies not residing in groups with the corrected richness of at least two M_B < −20.5 − z members, are shown in the right-hand panel in Figure 13 (red filled circles). We use the simple Equation (6) above, since the infall is a one-way depletion of the non-group population, again assuming that the infalling migrants are representative of the population as a whole.

Zoom In Zoom Out Reset image size

In a similar manner, we derive the rates of the color transformation from blue to red galaxies η_{B − >R} and from active to passive galaxies η_{A − >P} using the same group and non-group samples of galaxies as for measurements of η_{L − >E}. Galaxies are divided in different classes as in the previous subsection. The corresponding rates are overplotted in Figure 13 (using the green triangles for η_{B − >R} and violet squares for η_{A − >P}). Generally speaking, the rates obtained for the color and activity class transformation also show similar dependence on the mass and environment as the rates of the morphological transformation.

Comparison of the two panels of Figure 13 shows three interesting facts. (1) The rate of the class transformation is consistently higher in the group environment than outside of it. (2) The rate of transformation is consistently higher for the transformations involving star formation than for those involving morphological transformation. (3) The rate is higher for lower mass galaxies than for higher mass ones. Indeed the rates, and the differences between the rates inside and outside of groups, and between morphology and star formation, are all small and consistent with zero for the most massive galaxies above log(M_*/M_☉) ∼ 11.2. It should be noted that these rates must fall at still lower masses, beyond the range explored by zCOSMOS.

For typical galaxies with log(M_*/M_☉) ∼ 10.5, we conclude that the transformation rates are three to four times higher in the groups than outside, and are typically 50% higher for color transformations than for morphological ones. The implied transformation timescales η⁻¹, are of order 1.8 Gyr (color transformation) or 2.5 Gyr (morphology transformation) in the groups, and about 6 Gyr and 10 Gyr, respectively, outside of groups.

Needless to say, the exact values of the derived rates and corresponding timescales should be taken as indicative only. The quoted errors include only the purely statistical uncertainty. There are various other issues which one needs to be aware of. Although we have tried to deal with variations in N(z) due to the large-scale structure by considering fractions, the temporal gradients may be affected by the choice of redshift bins, since this will be affected by large-scale structure. At low z, the volume used for the analysis is the smallest, and the estimated fractions could be less representative of the universal values than the fractions estimated at higher redshifts, modifying the true slopes in the overall fractional evolution. Moreover, we have assumed constant rates (i.e., a linear evolution in the logarithmic fraction), and have furthermore estimated these at different epochs for the different mass ranges. We believe that the relative values should be more robust than the absolute ones.

It is fairly clear, e.g., comparing Figures 7 and 8, that the difference in the transformation rates computed here stem as much from the different fractions in the different environments (in the denominator) as from differences in the rate of change of the fractions (in the numerator), which are often rather similar. It is also clear that this difference in the fractions between the different environments amplifies the difference in implied transformational rates in the groups through infall correction, increasing the difference by about ∼50%. However, it is clear that this is not the sole origin of the rate difference between the different environments.

It should be noted that there are at least two effects that would act to reduce the observed rates, and therefore lead us to underestimate the effect of the group. First, as noted earlier in the paper, the non-group galaxies as we define them here, will be somewhat "polluted" by galaxies in small groups that are not yet detectable in the relatively sparse sampled zCOSMOS 10k sample. This will tend to wash out the environmental differences. This contamination will arise from the non-perfect isolation of the group sample in terms of the imperfect purity and completeness of the original group catalog. Second, we have implicitly assumed that the number of galaxies is conserved. Certainly in the case of morphological transformation, galaxy merging is a possible physical mechanism. It could well be that the merger of two late-type galaxies would produce only one early-type, and the implied change in the late-type fraction would then be smaller than if two early-type galaxies had been produced, leading to an underestimate in the transformation rate as defined in Equation (9). Against these, it should be remembered that the "infall correction," which also accounts for the appearance of new groups with time, will be a worst case scenario, because it assumes that the new group galaxies are drawn randomly from the earlier non-group population.

The derived transformation rates are of course closely linked to the mass functions given above (Figure 7). In particular, given the existence of the transition or crossing mass (where the population is split equally between the two types), and the evidence for the change of this with epoch, we would expect to see the highest transformation rates for galaxies around this same mass log(M_*/M_☉) ∼ 10.5 ± 0.5. At higher masses the transformation rates are lower because the population has saturated with most transformations completed, more than compensating for the small number of potential progenitor galaxies. At lower stellar masses, log(M_*/M_☉) ≲ 10, not presently accessible by the zCOSMOS observations, the transformation rates must drop again because the vast majority of galaxies are still in the pre-transformation state.

The effect of the environment modifying the transformation rates for star formation activity and color is larger than the environment's effect on the morphological rates, and we conclude that the environment seems to be more closely related to the star formation and color transformation processes than to the morphological transformation of galaxies. Similar conclusions have been obtained at z ∼ 0 when using much less direct diagnostics of the environmental influence (e.g., Kauffmann et al. 2004; Blanton et al. 2005; Skibba et al. 2009). For example, Blanton et al. (2005) and Skibba et al. (2009) show that galaxies of the same color do not have significant residual environmental dependence, while colors of galaxies of a given (similar) morphology still show environmental dependence.

This work has clearly demonstrated that, whatever physical processes are involved in the general transformations that are occurring in the galaxy population since z ∼ 1, especially around the transition or crossing mass, these processes are evidently much more effective in groups than outside of them. The transformation rate outside of groups is by no means zero, but might be lower than we have estimated because of residual contamination of the non-group population by group galaxies, as discussed above.

Our physical interpretation of the shorter timescales that we attribute to the color and/or star formation transitions, compared with those of the morphological transformations, is hindered by the uncertainty about whether the timescales involved are the physical timescales of the transitions (i.e., where t_p ∼ t_η), or what we have called the statistical timescales (where t_p ≪ t_s ∼ t_η), as discussed in Section 1. If dealing with prompt phenomena which have the same physical timescale, e.g., say the merging of galaxies, then we would want to interpret the difference in terms of different rates of this event, e.g., different merger rates. On the other hand, in the case of longer term processes, such as strangulation, the difference would be more naturally interpreted in terms of the speed with which the given process acts. Regardless, the fact that the transformation timescales vary rather strongly with galactic mass and with group/non-group environment, and also, but less strongly, with transition type, points toward a picture where a variety of physical processes may be operating.

The current sampling in the 10k zCOSMOS is about ∼30% on average, which is not sufficient to meaningfully split the population of the group galaxies into central and satellite galaxies, because two-thirds of the central galaxies will not have been observed spectroscopically. This will be much easier as the spectroscopic completeness doubles in the final 20k sample, especially if we also use the high quality photometric redshifts. Comparison with the mock group catalog (Knobel et al. 2009) suggests that both group and non-group samples (defined using M_B < −20.5 − z) are dominated by central galaxies.