The Escape of Globular Clusters from the Satellite Dwarf Galaxies of the
  Milky Way
  Using numerical simulations, we have studied the escape of globular clusters
(GCs) from the satellite dwarf spheroidal galaxies (dSphs) of the Milky Way
(MW). We start by following the orbits of a large sample of GCs around dSphs in
the presence of the MW potential field. We then obtain the fraction of GCs
leaving their host dSphs within a Hubble Time. We model dSphs by a Hernquist
density profile with masses between $10^7\,\mathrm{M}_{\odot}$ and $7\times
10^9\,\mathrm{M}_{\odot}$. All dSphs lie on the Galactic disc plane, but they
have different orbital eccentricities and apogalactic distances. We compute the
escape fraction of GCs from 13 of the most massive dSphs of the MW, using their
realistic orbits around the MW (as determined by Gaia). The escape fraction of
GCs from 13 dSphs is in the range $12\%$ to $93\%$. The average escape time of
GCs from these dSphs was less than 8 $\,\mathrm{Gyrs}$, indicating that the
escape process of GCs from dSphs was over. We then adopt a set of
observationally-constrained density profiles for specific case of the Fornax
dSph. According to our results, the escape fraction of GCs shows a negative
correlation with both the mass and the apogalactic distance of the dSphs, as
well as a positive correlation with the orbital eccentricity of dSphs. In
particular, we find that the escape fraction of GCs from the Fornax dSph is
between $13\%$ and $38\%$. Finally, we observe that when GCs leave their host
dSphs, their final orbit around the MW does not differ much from their host
dSphs.
