The Evolution of the Stellar Mass Function of Galaxies from Z = 4.0 and the First Comprehensive Analysis of Its Uncertainties: Evidence for Mass-dependent Evolution

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 NIR MUSYC, the FIRES, and the GOODS-CDFS 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 highmass 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 1010 M⊙ at z > 2. Taking our results at face value, we find that they are in conflict with semi-analytic 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. Subject headings: galaxies: distances and redshifts — galaxies: evolution — galaxies: formation — galaxies: fundamental parameters — galaxies: high-redshift — galaxies: luminosity function, mass function — galaxies: stellar content — infrared: galaxies