We present novel 3D multi-scale SPH simulations of gas-rich galaxy mergers between the most massive galaxies at $z sim 8 - 10$, designed to scrutinize the direct collapse formation scenario for massive black hole seeds proposed in citet{mayer+10}. Th
e simulations achieve a resolution of 0.1 pc, and include both metallicity-dependent optically-thin cooling and a model for thermal balance at high optical depth. We consider different formulations of the SPH hydrodynamical equations, including thermal and metal diffusion. When the two merging galaxy cores collide, gas infall produces a compact, optically thick nuclear disk with densities exceeding $10^{-10}$ g cm$^3$. The disk rapidly accretes higher angular momentum gas from its surroundings reaching $sim 5$ pc and a mass of $gtrsim 10^9$ $M_{odot}$ in only a few $10^4$ yr. Outside $gtrsim 2$ pc it fragments into massive clumps. Instead, supersonic turbulence prevents fragmentation in the inner parsec region, which remains warm ($sim 3000-6000$ K) and develops strong non-axisymmetric modes that cause prominent radial gas inflows ($> 10^4$ $M_{odot}$ yr$^{-1}$), forming an ultra-dense massive disky core. Angular momentum transport by non-axisymmetric modes should continue below our spatial resolution limit, quickly turning the disky core into a supermassive protostar which can collapse directly into a massive black hole of mass $10^8-10^9$ $M_{odot}$ via the relativistic radial instability. Such a cold direct collapse explains naturally the early emergence of high-z QSOs. Its telltale signature would be a burst of gravitational waves in the frequency range $10^{-4} - 10^{-1}$ Hz, possibly detectable by the planned eLISA interferometer.
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/sm
oothed 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.
