Dynamical Friction around Supermassive Black Holes
  The density of stars in galactic bulges is often observed to be flat or
slowly rising inside the influence radius of the supermassive black hole
(SMBH). Attributing the dynamical friction force to stars moving more slowly
than the test body, as is commonly done, is likely to be a poor approximation
in such a core since there are no stars moving more slowly than the local
circular velocity. We have tested this prediction using large-scale N-body
experiments. The rate of orbital decay never drops precisely to zero, because
stars moving faster than the test body also contribute to the frictional force.
When the contribution from the fast-moving stars is included in the expression
for the dynamical friction force, and the changes induced by the massive body
on the stellar distribution are taken into account, Chandrasekhar's theory is
found to reproduce the rate of orbital decay remarkably well. However, this
rate is still substantially smaller than the rate predicted by Chandrasekhar's
formula in its most widely-used forms, implying longer time scales for
inspiral. Motivated by recent observations that suggest a parsec-scale core
around the Galactic center SMBH, we investigate the evolution of a population
of stellar-mass black holes (BHs) as they spiral in to the center of the
Galaxy. After ~10Gyr, we find that the density of BHs can remain substantially
less than the density in stars at all radii; we conclude that it would be
unjustified to assume that the spatial distribution of BHs at the Galactic
center is well described by steady-state models. One consequence is that rates
of capture of BHs by the SMBH at the Galactic center (EMRIs) may be much lower
than in standard models. We finally study the orbital decay of satellite
galaxies into the central region of giant ellipticals and discuss the formation
of multiple nuclei and multiplet of black holes in such systems.
