Chaos and Variance in Galaxy Formation

The evolution of galaxies is governed by equations with chaotic solutions: gravity and compressible hydrodynamics. While this micro-scale chaos and stochasticity has been well studied, it is poorly understood how it couples to macro-scale properties examined in simulations of galaxy formation. In this paper, we show how perturbations introduced by floating-point roundoff, random number generators, and seemingly trivial differences in algorithmic behaviour can produce non-trivial differences in star formation histories, circumgalactic medium (CGM) properties, and the distribution of stellar mass. We examine the importance of stochasticity due to discreteness noise, variations in merger timings and how self-regulation moderates the effects of this stochasticity. We show that chaotic variations in stellar mass can grow until halted by feedback-driven self-regulation or gas exhaustion. We also find that galaxy mergers are critical points from which large (as much as a factor of 2) variations in quantities such as the galaxy stellar mass can grow. These variations can grow and persist for more than a Gyr before regressing towards the mean. These results show that detailed comparisons of simulations require serious consideration of the magnitude of effects compared to run-to-run chaotic variation, and may significantly complicate interpreting the impact of different physical models. Understanding the results of simulations requires us to understand that the process of simulation is not a mapping of an infinitesimal point in configuration space to another, final infinitesimal point. Instead, simulations map a point in a space of possible initial conditions points to a volume of possible final states.