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 ( \sim 10 ^ { 9 } \textrm { M } _ { \odot } ) and size ( \sim 60 \textrm { pc } ) in excellent agreement with previous SPH simulations with particle splitting that used a similar setup ( ) 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 } \textrm { 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 .
We believe that the rather ” hot ” Equation-of-State we used to model the multiphase turbulent ISM in the nuclear region is playing an important role in preventing efficient SMBH sinking inside the central parsec .
We conclude with a discussion of the way forward to address sinking in gaseous backgrounds at sub-pc scales approaching the gravitational wave regime .