  We present analytical and numerical solutions which describe a hot, viscous,
two-temperature accretion flow onto a neutron star or any other compact star
with a surface. We assume Coulomb coupling between the protons and electrons,
and free-free cooling from the electrons. Outside a thin boundary layer, where
the accretion flow meets the star, we show that there is an extended settling
region which is well-described by two self-similar solutions: (1) a
two-temperature solution which is valid in an inner zone $r\le10^{2.5}$ ($r$ is
in Schwarzchild units), and (2) a one-temperature solution at larger radii. In
both zones, $\rho\propto r^{-2}, \Omega\propto r^{-3/2}, v\propto r^0,\
T_p\propto r^{-1}$; in the two-temperature zone, $T_e\propto r^{-1/2}$. The
luminosity of the settling zone arises from the rotational energy of the star
as the star is braked by viscosity; hence the luminosity is independent of
$\dot M$. The settling solution is convectively and viscously stable and is
unlikely to have strong winds or outflows. The flow is thermally unstable, but
the instability may be stabilized by thermal conduction. The settling solution
described here is not advection-dominated, and is thus different from the
self-similar ADAF found around black holes. When the spin of the star is small
enough, however, the present solution transforms smoothly to a (settling) ADAF.
