Chaos and variance in galaxy formation

Abstract

The evolution of galaxies is governed by equations with chaotic solutions: gravity and compressible (magneto-)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 use tiny perturbations introduced by floating-point roundoff, random number generators, and seemingly trivial differences in algorithmic behaviour as seeds for chaotic behaviour. These can ultimately grow to 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 be suppressed through gas exhaustion, or be maintained at a roughly constant variance through stellar feedback. We also find that galaxy mergers are critical points from which large (as much as a factor of 2) variations can grow in global quantities such as the total stellar mass. These variations can grow and persist for Gyrs 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.

Calibration of a star formation and feedback model for cosmological simulations with enzo

“…Looking at Figure 14, the deviation in f s from the pair of simulations is comparable to the 10% difference in stellar mass concluded in Keller et al (2019) despite not using identical processors. However, the deviation in total baryon mass is as high as 33%, possibly arising from the coupling of star formation and feedback where a 10% difference in stellar mass affects the feedback significantly.…”

“…Recognising the argument put forth by Keller et al (2019) for chaotic variance in numerical simulations, we conduct our zoom simulations twice on different processors. They have identical initial conditions and feedback prescriptions but evolved on different combinations of processors in the same computing cluster.…”

“…In the absence of feedback, Genel et al (2018) highlighted differences in the properties of galaxies induced by very slight changes in the initial positions of dark matter particles. Even if a galaxy is evolved from identical initial conditions, the simulation code can introduce variances which result in fluctuations in the simulated properties between repetitions of the same simulation (Keller et al 2019). The problem is alleviated by the self-regulating nature of feedback (Keller et al 2019) and highlights the need to understand the impact that subgrid implementations have on the resulting properties of galaxies in simulations.…”

Forming early-type galaxies without AGN feedback: a combination of merger-driven outflows and inefficient star formation

“…There is a small difference in scalefactor for the starburst at a 0.65 which originates from slightly different trajectories caused by numerical effects (Keller et al 2019;Genel et al 2019). Furthermore, the efficiencies for the SN induced turbulence model in the quiescent phases is larger compared to the efficiencies in the SGS run.…”

The diversity and variability of star formation histories in models of galaxy evolution

“…While resolution can be a limiting factor in any analysis of small-scale features in hydrodynamical models, convergence tests on individual simulations (Genel et al 2018;Keller et al 2019). and forward modeling the effects of discrete star particles as in Appendix A allow us to understand and account for these limitations.…”