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