Dynamical friction and the evolution of Supermassive Black hole
  Binaries: the final hundred-parsec problem
  The supermassive black holes originally in the nuclei of two merging galaxies
will form a binary in the remnant core. The early evolution of the massive
binary is driven by dynamical friction before the binary becomes "hard" and
eventually reaches coalescence through gravitational wave emission. { We
consider the dynamical friction evolution of massive binaries consisting of a
secondary hole orbiting inside a stellar cusp dominated by a more massive
central black hole.} In our treatment we include the frictional force from
stars moving faster than the inspiralling object which is neglected in the
standard Chandrasekhar's treatment. We show that the binary eccentricity
increases if the stellar cusp density profile rises less steeply than
$\rho\propto r^{-2}$. In cusps shallower than $\rho\propto r^{-1}$ the
frictional timescale can become very long due to the deficit of stars moving
slower than the massive body. Although including the fast stars increases the
decay rate, low mass-ratio binaries ($q\lesssim 10^{-3}$) in sufficiently
massive galaxies have decay timescales longer than one Hubble time. During such
minor mergers the secondary hole stalls on an eccentric orbit at a distance of
order one tenth the influence radius of the primary hole (i.e., $\approx
10-100\rm pc$ for massive ellipticals). We calculate the expected number of
stalled satellites as a function of the host galaxy mass, and show that the
brightest cluster galaxies should have $\gtrsim 1$ of such satellites orbiting
within their cores. Our results could provide an explanation to a number of
observations, which include multiple nuclei in core ellipticals, off-center
AGNs and eccentric nuclear disks.
