The last few years have seen a flood of new observational data on large samples of galaxies, both locally, as in the SDSS and 2dfGRS and in large photometric and spectroscopic surveys at higher redshifts, such as COMBO-17, GOODS, DEEP, VVDS, COSMOS and zCOSMOS. These new surveys allow increasingly sophisticated statistical study of the overall properties of the population of galaxies, and its evolution over cosmic time. There has been much work also on developing a theory of galaxy evolution, mostly in the context of so-called semi-analytic models (SAMs) for the galaxy population, complemented by increasingly sophisticated hydro-dynamical simulations. Whichever approach is used, the evolution of galaxies is followed in a framework for the formation and evolution of dark matter haloes, to which are added simple analytic descriptions of all the relevant baryonic physics that can be imagined, including the heating and cooling of gas, the formation of stars, and the merging of galaxies.

The philosophy of this paper is to take a purely empirical, observationally-based, approach to the evolving galaxy population. In particular it is likely that galactic mass and environment are both playing a major role in the evolution of galaxies. Accordingly, we try to identify the most important relations of galaxy properties with mass and environment in the present-day galaxy population, and in the population at much earlier cosmic times. The goal is to use the observational material as directly as possible in order to identify the simplest things that are apparently demanded by the data and to define empirically based "laws" for the evolution of the population.

We introduce a new formalism to examine the differential effects of mass and Mpc-scale environment on the fraction of galaxies that have been quenched, fred(m,ρ), at a given mass and in a given environment. We demonstrate that the effects of mass and environment are fully separable in the SDSS sample (Figure 1), indicating that two distinct processes are occurring, which we refer to as "mass-quenching" and "environment-quenching". The effect of environment-quenching, at fixed over-density, evidently does not change with epoch to z ~ 1 in zCOSMOS, suggesting that the environment-quenching occurs as large scale structure develops in the Universe, probably through the cessation of star-formation in a fraction 30-70% of satellite galaxies. In contrast, mass-quenching appears to be a more dynamic process, governed by a quenching rate. We show that the observed constancy of the Schechter M* and α_s for star-forming galaxies, demands that the quenching of galaxies around and above M*, must follow a rate that is statistically proportional to their star-formation rates (or closely mimic such a dependence). We then postulate that this simple mass-quenching law in fact holds over a much broader range of stellar mass (2 dex) and cosmic time (essentially all epochs).

Figure 1.  Observed values of the relative mass quenching efficiency as a function of environment for different galaxy masses (top) in units of log solar mass, and of the relative environment quenching efficiency as a function of mass for different environments (bottom) in units of log (1+). The fact that these are essentially flat shows that the differential effects of mass and environment are separable in SDSS.

1. establishes a pure Schechter mass function for star-forming galaxies, and sets the characteristic mass M*;

2. produces a two-component Schechter mass function for passive galaxies, and for all galaxies (active plus passive) combined, and predicts well-defined relationships between the Schechter parameters of the various components that are observed in the galaxy population, with only small modifications due to some limited subsequent merging of galaxies;

3. accounts qualitatively for several other simple observational features of the galaxy population, such as the mean age-mass relation for passive galaxies and the α-enrichment of the more massive passive galaxies.

Subsequent merging of quenched galaxies will modify these predictions somewhat in the denser environments, mildly increasing M* and making α_s slightly more negative. All of these detailed predictions for the inter-relationships between the Schechter parameters of the star-forming and passive galaxies, across a broad range of environments, are indeed seen in the SDSS at the present epoch, lending strong support to our simple empirically-based model.

We then construct a simple simulation of the evolving galaxy population based on the remarkably simple picture outlined above, i.e. on just 3-4 observationally determined parameters, and show that from an initial starting point at z ~ 10 this successfully reproduces the mass-function and fred of the SDSS sample as a function of environment (Figure 2). Although the effects of dry-merging are on average small for the population of passive galaxies, with an average increase of mass of order 15% (assuming equal 1:1 mergers) to 40% (assuming highly asymmetric mergers) even in the densest D4 quartile, the importance of merging increases sharply with observed final mass, even for a merging rate that is independent of mass, simply because of the steepness of the mass function. The history of galaxies is summarized for passive galaxies in Fig 3, where we show, as a function of their final mass, the fraction of galaxies initially quenched through different mechanisms, and whether or not they have subsequently merged.

Figure 2.  Evolving mass-functions (top) and red fractions (bottom) for the simple model described in the text. The solid blue lines indicate the mass function of star-forming galaxies, the red lines represent the "mass-quenched" passive galaxies, and the dashed red lines show the "environment-quenched" and "merger-quenched" passive galaxies. The model is computed for the lowest density D1 quartile (left, shown for z =3, 2, 1, 0) and for the highest density D4 quartile (right, at z = 5, 3, 2, 1, 0, although the latter two blue mass-functions are completely overlapping). Also shown in all panels are the low redshift observational data from the SDSS survey. The black line in the left-hand panel shows also the model prediction and SDSS data for all galaxies (regardless of environment). In each environment, the model is normalized in total number to the SDSS data. A movie based on this figure can be found: http://www.exp-astro.phys.ethz.ch/zCOSMOS/MF_simulation_d1_d4.mov

Figure 3.  Diagram summarizing the evolutionary histories of today's passive galaxies (summed over all environments) as a function of their final stellar mass. The colors represent different modes by which the passive galaxies were initially quenched, i.e. mass-quenching (red), environment-quenching (blue) and merger-quenching (green). The color shades then represent whether the galaxy subsequently underwent a merger (yes, light, or no, deep). The effect of post-quenching merging on environment-quenched galaxies is small, because most environment-quenching takes place after the merging rate has declined (see Fig 15 in the paper). Although the amount of post-quenching merging of mass-quenched galaxies is quite small (only a few % in the overall galaxy population), and although the rate of merging is assumed to be independent of mass, the steepness of the mass function above M* means that dry-merging will have been progressively more important in the most massive galaxies above 10¹¹ M_.

For more information, see http://arxiv.org/abs/1003.4747 Y. Peng, S.J. Lilly, K. Kovac and zCOSMOS collaboration; submitted to ApJ