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.