A Quantification of the Butterfly Effect in Cosmological Simulations and Implications for Galaxy Scaling Relations

Abstract

We study the chaotic-like behavior of cosmological simulations by quantifying how minute perturbations grow over time and manifest as macroscopic differences in galaxy properties. When we run pairs of 'shadow' simulations that are identical except for random minute initial displacements to particle positions (e.g. of order 10 −7 pc), the results diverge from each other at the individual galaxy level (while the statistical properties of the ensemble of galaxies are unchanged). After cosmological times, the global properties of pairs of 'shadow' galaxies that are matched between the simulations differ from each other generally at a level of ∼ 2 − 25%, depending on the considered physical quantity. We perform these experiments using cosmological volumes of (25 − 50 Mpc/h) 3 evolved either purely with dark matter, or with baryons and star-formation but no feedback, or using the full feedback model of the IllustrisTNG project. The runs cover four resolution levels spanning a factor of 512 in mass. We find that without feedback the differences between shadow galaxies generally become smaller as the resolution increases, but with the IllustrisTNG model the results are mostly converging toward a 'floor'. This hints at the role of feedback in setting the chaotic properties of galaxy formation. Importantly, we compare the macroscopic differences between shadow galaxies to the overall scatter in various galaxy scaling relations, and conclude that for the star formation-mass and the Tully-Fisher relations the butterfly effect in our simulations contributes significantly to the overall scatter. We find that our results are robust to whether random numbers are used in the subgrid models or not. We discuss the implications for galaxy formation theory in general and for cosmological simulations in particular.

The effect of magnetic fields on properties of the circumgalactic medium

“…Owing to the chaotic nature of galaxy formation, we do not expect results to be identical. Stellar masses are within 0.04 dex of one another for the simulations with different refinement methods and black hole masses within 0.07 dex, consistent with expectations from the butterfly effect (Genel et al 2019). The differences and similarities between properties with and without magnetic fields described in Section 3 are reproduced by the simulations without CGM refinement.…”

Quenching and morphological evolution due to circumgalactic gas expulsion in a simulated galaxy with a controlled assembly history

“…In the limit of adequate sampling, the influence of the intrinsic uncertainty associated with stochastic implementations diminishes, such that the properties of the galaxy population in a cosmic volume are, in a statistical sense, agnostic to the choice of the initial seed used by the quasi-random number generator. However, when considering the evolution of individual objects (as is the case here), this uncertainty can in principle be significant (Keller et al 2020), and appears to be increasingly severe with decreasing resolution (Genel et al 2019).…”

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.…”