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Using N-body/SPH simulations we study the evolution of the separation of apair of SMBHs embedded in a star forming circumnuclear disk (CND). This type ofdisk is expected to be formed in the central kilo parsec of the remnant ofgas-rich galaxy mergers. Our simulations indicate that orbital decay of theSMBHs occurs more quickly when the mean density of the CND is higher, due toincreased dynamical friction. However, in simulations where the CND isfragmented in high density gaseous clumps (clumpy CND), the orbits of the SMBHsare erratically perturbed by the gravitational interaction with these clumps,delaying, in some cases, the orbital decay of the SMBHs. The densities of thesegaseous clumps in our simulations and in recent studies of clumpy CNDs aresignificantly higher than the observed density of molecular clouds in isolatedgalaxies or ULIRGs, thus, we expect that SMBH orbits are perturbed less in realCNDs than in the simulated CNDs of this study and other recent studies. We alsofind that the migration timescale has a weak dependence on the star formationrate of the CND. Furthermore, the migration timescale of a SMBH pair in astar-forming clumpy CND is at most a factor three longer than the migrationtimescale of a pair of SMBHs in a CND modeled with more simple gas physics.Therefore, we estimate that the migration timescale of the SMBHs in a clumpyCND is on the order of $10^7$ yrs.

Super massive black holes in star forming gaseous circumnuclear discs