The effect of a disc on the population of cuspy and cored dark matter
  substructures in Milky Way-like galaxies
  We use high-resolution $N$-body simulations to study the effect of a galactic
disc on the dynamical evolution of dark matter substructures with orbits and
structural parameters extracted from the Aquarius A-2 merger tree (Springel et
al. 2008). Satellites are modelled as equilibrium $N$-body realizations of
generalized Hernquist profiles with $2\times10^6$ particles and injected in the
analytical evolving host potential at $z_\mathrm{infall}$, defined by the peak
of their mass evolution. We select all substructures with
$M_{200}(z_\mathrm{infall})\geq 10^8\,\mathrm{M_\odot}$ and first pericentric
distances $r_p<r_{200}$. Motivated by observations of Milky Way dwarf
spheroidal galaxies, we also explore satellite models with cored dark matter
profiles with a fixed core size $r_c=0.8\,a_s$ where $a_s$ is the Hernquist
scale radius. We find that models with cuspy satellites have twice as many
surviving substructures at $z=0$ than their cored counterparts, and four times
as many if we only consider those on orbits with $r_p\lesssim0.1\,r_{200}$. For
a given profile, adding an evolving disc potential reduces the number of
surviving substructures further by a factor of $\lesssim2$ for satellites on
orbits that penetrate the disc ($r_p\lesssim 20\,\mathrm{kpc}$). For large
$r_p$, where tidal forces and the effect of the disc become negligible, the
number of satellites per pericentre bin converges to similar values for all
four models.
