Under the sword of Damocles: plausible regeneration of dark matter cusps at the smallest galactic scales

Abstract

We run controlled N-body experiments to study the evolution of the dark matter (DM) halo profiles of dwarf galaxies driven by the accretion of DM substructures. Our initial conditions assume that supernova feedback erases the primordial DM cusps of haloes with $10^{9}-10^{10} \rm{M_{\odot}}$ at $z=0$. The orbits and masses of the infalling substructures are borrowed from the {\it Aquarius} simulations. Our experiments show that a fraction of haloes that undergo 1:3 down to 1:30 mergers are susceptible to reform a DM cusp by $z\approx 0$. Cusp regrowth is driven the accretion of DM substructures that are dense enough reach the central regions of the main halo before being tidally disrupted. The infall of substructures with a mass ratio above 1:6 on the mean of the reported mass-concentration relation systematically lead to cusp regrowth. Between 1:6 to 1:8, and 1:8 to 1:30 substructures need to be located one and two-sigma above the mean, respectively. The merging timescales of these dense, low-mass substructures is relatively long $(5-11 \rm{Gyrs})$, which may pose a timescale problem for the longevity of DM cores in dwarf galaxies. These results suggest that a certain level of scatter in the central density slopes of galactic haloes acted-on by feedback is to be expected given the stochastic mass accretion histories of low-mass haloes and the diverse star formation histories observed in the Local Group dwarves.