Over the last 15 years extensive surveys of high-redshift galaxy evolution (e.g., GOODS, UDF, COSMOS, AEGIS and CANDELS) with space- and ground-based telescopes have dramatically increased our understanding of galaxy evolution in the early universe. All of these go very deep (typically > 27-30 mag AB) but cover very different size areas - most also have excellent multi-wavelength, ancillary data. The largest survey (COSMOS) has over a million galaxies with photometry and photometric redshifts at z = 0.2-6 and the deepest (UDF) now has detections at z = 6-8, probing the first 1 Gyr of cosmic time. Major evolution is seen in the galaxy properties: stellar mass, luminosity, size and SFR.
8.4.1. Luminosity and Mass Functions
Figure 8.25 shows a compilation of recent determinations of the z = 4-6 luminosity functions (LFs; Capak et al. 2011). Evolution of the UV LF (probing the distribution of star-forming galaxies) is clearly seen with the number densities increasing at all luminosities as one goes to lower redshift and there is apparent steepening of the low-L power law going to higher redshift, i.e., more low-luminosity galaxies contributing. If this persists to higher redshift then it can be argued that the reionisation of the universe at z ~ 10 must have been produced by relatively low-luminosity galaxies (Robertson et al. 2010). At z > 6, the samples are very small, ~ 20-50 objects with virtually no spectroscopic confirmation. Even at z = 6, one can see large scatter in the different determinations of the LF, shown as points in Fig. 8.25. It is noteworthy that the high-L portion of the LF is very poorly constrained (see Fig. 8.25) and could even be a power law rather than the Schechter function (exponential fall-off) used in fitting.
 |
Figure 8.25. A compilation of z = 4 and 6 UV LFs for galaxies (Capak et al. 2011). The curves are Schechter function fits by Bouwens et al. (2007) for z = 4 (blue) and 6 (black) galaxies and the points are derived for Lyman alpha emitters (LAEs) and Lyman break galaxies (LBGs). |
At lower redshifts, comparatively good samples exist for the stellar mass functions of galaxies (see Fig. 8.26). Strong growth in the number density of galaxies at all masses is seen but the largest increase at late epochs (low z) occurs in the lower-mass galaxies (see, e.g., Ilbert et al. 2010). This `downsizing' of evolution at later epochs is also seen in the galaxies with star formation and AGN activity.
 |
Figure 8.26. The stellar mass function for galaxies at z = 0.1-4 from Marchesini et al. (2009). |
In principle, the buildup of stellar mass in galaxies as a function of time should be consistent with the evolution of star formation activity within galaxies in each mass bin. Discrepancies between these two might indicate the rate of galactic merging (assuming the masses and SFRs are reliable). This has been explored by Drory & Alvarez (2008) who find reasonable consistency between the stellar mass buildup and the SFR evolution - providing the SFRs drop first in the highest-mass galaxies and galaxies typically undergo ~ 1 major merger after z = 1.5 (see also Reddy 2011).
8.4.2. Environmental correlations
In 
CDM simulations
for the early Universe, it is the most massive,
highly biased, structures which form earliest. Such structures will
become the locations of massive galaxy clusters with the most massive
galaxies built there first. The COSMOS survey
(Scoville et al.
2007b)
was specifically
designed to probe a sufficiently large area on the sky (2 square degrees
corresponding to 
50-100 comoving Mpc at z > 0.5) that the full
range of environmental densities could be sampled at all redshifts. This
enables both the mapping of the large-scale structure and the
investigation of the correlation of galaxy evolution with
environment. High-accuracy photometric redshifts and a large sample of
spectroscopic redshifts enable the separation of galaxy structures along
the line of sight. Figure 8.27 shows the 200
overdense regions of galaxies seen in COSMOS at z = 0.1-2.55
(Scoville et al.
2012).
 |
Figure 8.27. Large-scale structures mapped
by the projected density of galaxies in redshift slices
( |
Using the environmental densities shown in Fig. 8.27, I show the percentage of early-type galaxies (with SED corresponding to E-Sa galaxies) as a function of density and redshift in Fig. 8.28 (left panel). As is well known from many studies, the early-type galaxy fraction increases systematically to a fraction ~ 50% at z = 0. However, Fig. 8.28 (left panel) also clearly isolates the differential evolution associated with large-scale structure density - the early-type galaxies form first in the highest-density regions of the large-scale structure.
 |
Figure 8.28. Left panel: the early-type (E-Sa) galaxy fraction is clearly correlated with both redshift and large-scale structure density from Fig. 8.27 (Scoville et al. 2007a; Scoville et al. 2012). The early-type galaxies form first in the highest-density environments. Right panel: the percentage of the overall SFRD is shown as a function of redshift and large-scale structure density. The dominant environments for star formation shift to lower density at later epochs (Scoville et al. 2012). |
The evolution of the SFR density (SFRD = SFR per comoving volume) rises a factor 20 from z = 0 to a peak at z = 2-3. An important question is: in which environments is the star formation occurring at each epoch? Figure 8.28 (right panel) shows that the SFRD systematically shifts from dense to less dense regions of the large-scale structure as time progresses. Peng et al. (2010), using both COSMOS and SDSS data, show that the quenching of star formation activity in galaxies has two separable terms: one dependent on galaxy mass and the other on environmental density.
Recently, Rodighiero et al. (2011) have attempted to quantify the fraction of star formation occurring in starbursts versus normal-rate star formation at z = 1.5-2.5. They make use of a BZK colour-selected sample of galaxies with low SFR and samples from GOODS and COSMOS, probing with Herschel and Spitzer the moderate- and high-FIR luminosity galaxies (see Fig. 8.29). The BZK galaxies are used to define a `main sequence' of star-forming galaxies at this epoch. The outliers above the main sequence (mostly IR-detected) with more than four times the SSFR are then taken to be galaxies undergoing burst-mode star formation. Rodighiero et al. (2011) suggest that only 2% of the galaxies by number are undergoing starbursts and this population contributes ~ 10% of the total SFRD at this epoch. This is an interesting approach to the issue, but it should be clear that the adopted definition of the main sequence and its spread will entirely determine the starburst percentages. In addition, some of the galaxies within the main sequence could well be merger-starbursts of originally lower-SSFR galaxies. As noted earlier, it would be advantageous to have a physically-based definition of bursting rather than simply picking outliers as bursts. To take an extreme example, the latter definition would clearly be wrong if essentially a large fraction of the population were, in fact, bursting.
 |
Figure 8.29. The SFRs of three samples of galaxies at z = 1.5-2.5 and stellar masses are shown (Rodighiero et al. 2011). The samples include BZK-selected galaxies (black dots), GOODS (cyan) data and COSMOS (red) galaxies with Hershel PACS FIR detection. They use the BZK galaxies to define a `main sequence' of star-forming galaxies at this epoch and then classify the outlier (mostly IR-detected) galaxies at > 4 times the SSFR on the main sequence as starburst-mode galaxies. |
z =
0.02-0.2) in the COSMOS survey field
(