Numerical simulations of dark matter haloes produce polytropic central cores when reaching thermodynamic equilibrium

TL;DR

This paper demonstrates that dark matter haloes develop polytropic cores when reaching thermodynamic equilibrium, explaining the presence of cores in simulations with collisional interactions and their absence in collisionless CDM.

Contribution

It shows that cores in dark matter haloes are consistent with thermodynamic equilibrium and that numerical artifacts or self-interactions lead to their formation, unifying theory and simulations.

Findings

Cores form in simulations when collisions are allowed or artificially enhanced.

Cores have polytropic density profiles matching theoretical expectations.

Discrepancies in core presence are due to collisional effects and numerical artifacts.

Abstract

Self-gravitating astronomical objects often show a central plateau in the density profile (core) whose physical origin is hotly debated. Cores are theoretically expected in N-body systems of maximum entropy, however, they are not present in the canonical N-body numerical simulations of cold dark matter (CDM). Our work shows that despite this apparent contradiction between theory and numerical simulations, they are fully consistent. Simply put, cores are characteristic of systems in thermodynamic equilibrium, but thermalizing collisions are purposely suppressed in CDM simulations. When collisions are allowed, N-body numerical simulations develop cored density profiles, in perfect agreement with the theoretical expectation. We compare theory and two types of numerical simulations: (1) when DM particles are self-interacting (SIDM) with enough cross-section, then the effective two-body relaxation timescale becomes shorter than the Hubble time resulting in cored DM haloes. The haloes thus obtained, with masses from dwarf galaxies to galaxy clusters, collapse to a single shape after normalization, and this shape agrees with the polytropic density profile theoretically expected. (2) The inner radii in canonical N-body numerical simulations are always discarded because the use of finite-mass DM particles artificially increases the two-body collision rate. We show that the discarded radii develop cores that are larger than the employed numerical softening and have polytropic shapes independently of halo mass. Our work suggests that the presence of cores in simulated (or observed) density profiles can used as evidence for systems in thermodynamic equilibrium.