Massive black hole pairs in clumpy, self-gravitating circumnuclear
  disks: stochastic orbital decay
  We study the dynamics of massive black hole pairs in clumpy gaseous
circumnuclear disks. We track the orbital decay of the light, secondary black
hole $M_{\bullet2}$ orbiting around the more massive primary at the center of
the disk, using $N$-body/smoothed particle hydrodynamic simulations. We find
that the gravitational interaction of $M_{\bullet2}$ with massive clumps
$M_{\rm cl}$ erratically perturbs the otherwise smooth orbital decay. In close
encounters with massive clumps, gravitational slingshots can kick the secondary
black hole out of the disk plane. The black hole moving on an inclined orbit
then experiences the weaker dynamical friction of the stellar background,
resulting in a longer orbital decay timescale. Interactions between clumps can
also favor orbital decay when the black hole is captured by a massive clump
which is segregating toward the center of the disk. The stochastic behavior of
the black hole orbit emerges mainly when the ratio $M_{\bullet2}/M_{\rm cl}$
falls below unity, with decay timescales ranging from $\sim1$ to $\sim50$ Myr.
This suggests that describing the cold clumpy phase of the inter-stellar medium
in self-consistent simulations of galaxy mergers, albeit so far neglected, is
important to predict the black hole dynamics in galaxy merger remnants.
