We present measurements of the stellar mass functions (SMFs) of star-forming and quiescent galaxies to z = 4 using a sample of 95 675 galaxies in the COSMOS/UltraVISTA field. Sources have been selected from the DR1 UltraVISTA K s -band imaging which covers a unique combination of a wide area (1.62 deg 2 ), to a significant depth (K s,tot = 23.4, 90% completeness). The SMFs of the combined population are in good agreement with previous measurements and show that the stellar mass density of the universe was only 50%, 10% and 1% of its current value at z ∼ 0.75, 2.0, and 3.5, respectively. The quiescent population drives most of the overall growth, with the stellar mass density of these galaxies increasing as ρ star ∝ (1 + z) −4.7±0.4 since z = 3.5, whereas the mass density of star-forming galaxies increases as ρ star ∝ (1 + z) −2.3±0.2 . At z > 2.5, star-forming galaxies dominate the total SMF at all stellar masses, although a nonzero population of quiescent galaxies persists to z = 4. Comparisons of the K s -selected star-forming galaxy SMFs to UV-selected SMFs at 2.5 < z < 4 show reasonable agreement and suggests UV-selected samples are representative of the majority of the stellar mass density at z > 3.5. We estimate the average mass growth of individual galaxies by selecting galaxies at fixed cumulative number density. The average galaxy with Log(M * /M ⊙ ) = 11.5 at z = 0.3 has grown in mass by only 0.2 dex (0.3 dex) since z = 2.0(3.5), whereas those with Log(M * /M ⊙ ) = 10.5 have grown by > 1.0 dex since z = 2. At z < 2, the time derivatives of the mass growth are always larger for lower-mass galaxies, which demonstrates that the mass growth in galaxies since that redshift is mass-dependent and primarily bottom-up. Lastly, we examine potential sources of systematic uncertainties on the SMFs and find that those from photo-z templates, SPS modeling, and the definition of quiescent galaxies dominate the total error budget in the SMFs.

The 3D-HST and CANDELS programs have provided WFC3 and ACS spectroscopy and photometry over ≈ 900 arcmin 2 in five fields: AEGIS, COSMOS, GOODS-North, GOODS-South, and the UKIDSS UDS field. All these fields have a wealth of publicly available imaging datasets in addition to the HST data, which makes it possible to construct the spectral energy distributions (SEDs) of objects over a wide wavelength range. In this paper we describe a photometric analysis of the CANDELS and 3D-HST HST imaging and the ancillary imaging data at wavelengths 0.3 µm -8 µm. Objects were selected in the WFC3 near-IR bands, and their SEDs were determined by carefully taking the effects of the point spread function in each observation into account. A total of 147 distinct imaging datasets were used in the analysis. The photometry is made available in the form of six catalogs: one for each field, as well as a master catalog containing all objects in the entire survey. We also provide derived data products: photometric redshifts, determined with the EAZY code, and stellar population parameters determined with the FAST code. We make all the imaging data that were used in the analysis available, including our reductions of the WFC3 imaging in all five fields. 3D-HST is a spectroscopic survey with the WFC3 and ACS grisms, and the photometric catalogs presented here constitute a necessary first step in the analysis of these grism data. All the data presented in this paper are available through the 3D-HST website. 16

Several recent studies have shown that about half of the massive galaxies at z ∼ 2 are in a quiescent phase. Moreover, these galaxies are commonly found to be ultra-compact with half-light radii of ∼ 1 kpc. We have obtained a ∼ 29 hr spectrum of a typical quiescent, ultra-dense galaxy at z = 2.1865 with the Gemini Near-Infrared Spectrograph. The spectrum exhibits a strong optical break and several absorption features, which have not previously been detected in z > 2 quiescent galaxies. Comparison of the spectral energy distribution with stellar population synthesis models implies a low star formation rate (SFR) of 1-3 M yr −1 , an age of 1.3-2.2 Gyr, and a stellar mass of ∼ 2×10 11 M . We detect several faint emission lines, with emission-line ratios of [N ii]/Hα, [S ii]/Hα, and [O ii]/[O iii] typical of low-ionization nuclear emission-line regions. Thus, neither the stellar continuum nor the nebular emission implies active star formation. The current SFR is < 1% of the past average SFR. If this galaxy is representative of compact quiescent galaxies beyond z = 2, it implies that quenching of star formation is extremely efficient and also indicates that low luminosity active galactic nuclei (AGNs) could be common in these objects. Nuclear emission is a potential concern for the size measurement. However, we show that the AGN contributes 8% to the rest-frame optical emission. A possible post-starburst population may affect size measurements more strongly; although a 0.5 Gyr old stellar population can make up 10% of the total stellar mass, it could account for up to ∼ 40% of the optical light. Nevertheless, this spectrum shows that this compact galaxy is dominated by an evolved stellar population.

We study the growth of massive galaxies from z = 2 to the present using data from the NEWFIRM Medium Band Survey (NMBS). The sample is selected at a constant number density of n = 2 × 10 −4 Mpc −3 , so that galaxies at different epochs can be compared in a meaningful way. We show that the stellar mass of galaxies at this number density has increased by a factor of ≈ 2 since z = 2, following the relation log M n (z) = 11.45 − 0.15z. In order to determine at what physical radii this mass growth occurred we construct very deep stacked restframe R band images of galaxies with masses near M n (z), at redshifts z = 0.6, 1.1, 1.6, and 2.0. These image stacks of typically 70-80 galaxies enable us to characterize the stellar distribution to surface brightness limits of ∼ 28.5 mag arcsec −2 . We find that massive galaxies gradually built up their outer regions over the past 10 Gyr. The mass within a radius of r = 5 kpc is nearly constant with redshift whereas the mass at 5 kpc < r < 75 kpc has increased by a factor of ∼ 4 since z = 2. Parameterizing the surface brightness profiles we find that the effective radius and Sersic n parameter evolve as r e ∝ (1 + z) −1.3 and n ∝ (1 + z) −1.0 respectively. The data demonstrate that massive galaxies have grown mostly inside-out, assembling their extended stellar halos around compact, dense cores with possibly exponential radial density distributions. Comparing the observed mass evolution to the average star formation rates of the galaxies we find that the growth is likely dominated by mergers, as insitu star formation can only account for ∼ 20 % of the mass build-up from z = 2 to z = 0. A direct consequence of these results is that massive galaxies do not evolve in a self-similar way: their structural profiles change as a function of redshift, complicating analyses which (often implicitly) assume self-similarity. The main uncertainties in this study are possible redshift-dependent systematic errors in the total stellar masses and the conversion from light-weighted to mass-weighted radial profiles.

We present the evolution of the stellar mass function (SMF) of galaxies from z = 4.0 to z = 1.3 measured from a sample constructed from the deep near-infrared Multi-wavelength Survey by Yale-Chile, the Faint Infrared Extragalactic Survey, and the Great Observatories Origins Deep Survey-Chandra Deep Field South surveys, all having very high-quality optical to mid-infrared data. This sample, unique in that it combines data from surveys with a large range of depths and areas in a self-consistent way, allowed us to (1) minimize the uncertainty due to cosmic variance and empirically quantify its contribution to the total error budget; (2) simultaneously probe the high-mass end and the low-mass end (down to ∼0.05 times the characteristic stellar mass) of the SMF with good statistics; and (3) empirically derive the redshift-dependent completeness limits in stellar mass. We provide, for the first time, a comprehensive analysis of random and systematic uncertainties affecting the derived SMFs, including the effect of metallicity, extinction law, stellar population synthesis model, and initial mass function. We find that the mass density evolves by a factor of ∼17 +7 −10 since z = 4.0, mostly driven by a change in the normalization Φ . If only random errors are taken into account, we find evidence for mass-dependent evolution, with the low-mass end evolving more rapidly than the high-mass end. However, we show that this result is no longer robust when systematic uncertainties due to the SED-modeling assumptions are taken into account. Another significant uncertainty is the contribution to the overall stellar mass density of galaxies below our mass limit; future studies with WFC3 will provide better constraints on the SMF at masses below 10 10 M at z > 2. Taking our results at face value, we find that they are in conflict with semianalytic models of galaxy formation. The models predict SMFs that are in general too steep, with too many low-mass galaxies and too few high-mass galaxies. The discrepancy at the high-mass end is susceptible to uncertainties in the models and the data, but the discrepancy at the low-mass end may be more difficult to explain.