We study the formation of a supermassive black hole (SMBH) binary and the
shrinking of the separation of the two holes to sub-pc scales starting from a
realistic major merger between two gas-rich spiral galaxies with mass
comparable to our Milky Way. The simulations, carried out with the Adaptive
Mesh Refinement (AMR) code RAMSES, are capable of resolving separations as
small as 0.1 pc. The collision of the two galaxies produces a gravo-turbulent
rotating nuclear disk with mass (10^9 Msun) and size (60 pc) in excellent
agreement with previous SPH simulations with particle splitting that used a
similar setup (Mayer et al. 2007) but were limited to separations of a few
parsecs. The AMR results confirm that the two black holes sink rapidly as a
result of dynamical friction onto the gaseous background, reaching a separation
of 1 pc in less than 10^7 yr. We show that the dynamical friction wake is well
resolved by our model and we find good agreement with analytical predictions of
the drag force as a function of the Mach number. Below 1 pc, black hole pairing
slows down significantly, as the relative velocity between the sinking SMBH
becomes highly subsonic and the mass contained within their orbit falls below
the mass of the binary itself, rendering dynamical friction ineffective. In
this final stage, the black holes have not opened a gap as the gaseous
background is highly pressurized in the center. Non-axisymmetric gas torques do
not arise to restart sinking in absence of efficient dynamical friction, at
variance with previous calculations using idealized equilibrium nuclear disk
models. (abridged)Comment: Accepted for publication in MNRAS. 10 pages, 6 figure
