Quasistatic Equlibrium Models of Galaxy Formation and the Consequences of Stochasticity: The Central Limit Theorem, Memory, and Precision Galaxy Evolution from First Principles

Tue, May 12, 2015

Incomplete knowledge of fundamental aspects of astrophysics severely limits the realism and accuracy of star-formation histories in simulations, resulting in poorly modeled correlations of galaxy properties with mass and environment, hampering our understanding of how galaxy populations have evolved for the past 13 Gyr. We have now derived new insights from the observed correlation of star-formation rates with stellar mass, dubbed the "main sequence of star-formation." Modern mathematics allows us to newly understand that this correlation is emergent, not deterministic. I will demonstrate that SFMS is a simple consequence of the central limit theorem for systems in quasi-static equilibria, of the kinds described by models in which gas inflow and feedback are nearly in balance for long periods of time. For fair, unbiased samples of (disk) galaxies, we derive an expectation that the median of SFR/Integral(SFR) is independent of mass, identically equal to 2/t, and has a relative scatter that is also independent of mass and time.  This radically new mathematical framework reproduces, with no prior inputs, several important observables, including the early evolution of galaxy mass functions and the star-formation rate density, the median/mean SSFRs of galaxies on the "flat part" of the SFMS over 0 < z < 10, as well as published estimates of the scatter in SSFR at fixed mass and redshift. Modern mathematics now provides tools by which we can successfully model the ensembles of galaxies, constructing exact distributions of galaxy star-formation and assembly histories over the full extent of cosmic time.