  Based on the observed paucity of the dwarf spheroidal (dSph) satellites of
the Milky Way at small Galactocentric distances, we put forward the hypothesis
that subsequent to the formation of the Milky Way and its satellites, those
dSphs that had orbits with small perigalacticons were tidally disrupted,
leaving behind a population that now has a relatively larger value of its
average perigalacticon to apogalacticon ratio and consequently a larger value
of its r.m.s. transverse to radial velocities ratio compared to their values at
the time of formation of the dSphs. We analyze the implications of this
hypothesis for the phase space distribution of the dSphs and that of the dark
matter (DM) halo of the Galaxy within the context of a self-consistent model in
which the functional form of the phase space distribution of DM particles
follows the King model i.e. the `lowered isothermal' distribution and the
potential of the Galaxy is determined self-consistently by including the
gravitational cross-coupling between visible matter and DM particles. This
analysis, coupled with virial arguments, yields an estimate of $\gsim$ 270 km/s
for the circular velocity of any test object at galactocentric distances of
$\sim$ 100 kpc, the typical distances of the dSphs. The corresponding
self-consistent values of the relevant DM halo model parameters, namely, the
local (i.e., the solar neighbourhood) values of the DM density and velocity
dispersion in the King model and its truncation radius, are estimated to be
$\sim$ 0.3 GeV/cm^3, >350 km/s and $\gsim$ 150 kpc, respectively. Similar
self-consistent studies with other possible forms of the DM distribution
function will be useful in assessing the robustness of our estimates of the
Galaxy's DM halo parameters.
