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On the Origin and Evolution of the Galaxy Stellar Mass Function

Here we explore the evolution of galaxy ensembles at early times by writing the in situ stellar mass growth of galaxies purely as a stationary stochastic (e.g., quasi-steady state) process. By combining the mathematics of such processes with Newtonian gravity and a mean local star formation efficiency, we show that the stellar mass evolution of galaxy ensembles is directly related to the average acceleration of baryons onto dark matter halos at the onset of star formation, with explicit dependencies on initial local matter densities and halo mass. The density term specifically implies more rapid average rates of growth in higher density regions of the universe compared to low density regions, i.e., assembly bias. With this framework, using standard cosmological parameters, a mean star formation efficiency derived by other authors, and knowledge of the shape of the cosmological matter power spectrum at small scales, we analytically derive (1) the characteristic stellar masses of galaxies (M*), (2) the power-law low-mass slope (alpha) and normalization (phi*) of the stellar mass function, and (3) the evolution of the stellar mass function in time over 12.5 > z > 2. Correspondingly, the rise in the cosmic star formation rate density over these epochs, while the universe can sustain unabated fueling of star formation, also emerges naturally. All of our findings are consistent with the deepest available data, including the expectation of alpha~-7/5; i.e., a stellar mass function low-mass slope that is notably shallower than that of the halo mass function, and with no systematic deviations from a mean star formation efficiency with density or mass, nor any explicit, additional feedback mechanisms. These derivations yield a compelling richness and complexity but also show that very few astrophysical details are required to understand the evolution of cosmic ensemble of galaxies at early times.