  (Abridged) We review the results of the first multi-scale, hydrodynamical
simulations of mergers between galaxies with central supermassive black holes
(SMBHs) to investigate the formation of SMBH binaries in galactic nuclei. We
demonstrate that strong gas inflows produce nuclear disks at the centers of
merger remnants whose properties depend sensitively on the details of gas
thermodynamics. In numerical simulations with parsec-scale spatial resolution
in the gas component and an effective equation of state appropriate for a
starburst galaxy, we show that a SMBH binary forms very rapidly, less than a
million years after the merger of the two galaxies. Binary formation is
significantly suppressed in the presence of a strong heating source such as
radiative feedback by the accreting SMBHs. We also present preliminary results
of numerical simulations with ultra-high spatial resolution of 0.1 pc in the
gas component. These simulations resolve the internal structure of the
resulting nuclear disk down to parsec scales and demonstrate the formation of a
central massive object (~ 10^8 Mo) by efficient angular momentum transport.
This is the first time that a radial gas inflow is shown to extend to parsec
scales as a result of the dynamics and hydrodynamics involved in a galaxy
merger, and has important implications for the fueling of SMBHs. Due to the
rapid formation of the central clump, the density of the nuclear disk decreases
significantly in its outer region, reducing dramatically the effect of
dynamical friction and leading to the stalling of the two SMBHs at a separation
of ~1 pc. We discuss how the orbital decay of the black holes might continue in
a more realistic model which incorporates star formation and the multi-phase
nature of the ISM.
