Off the Beaten Path: A New Approach to Realistically Model The Orbital Decay of Supermassive Black Holes in Galaxy Formation Simulations

We introduce a force correction term to better model the dynamical friction (DF) experienced by a supermassive black hole (SMBH) as it orbits within its host galaxy. This new approach accurately follows the orbital decay of a SMBH and drastically improves over commonly used advection methods. The force correction introduced here naturally scales with the force resolution of the simulation and converges as resolution is increased. In controlled experiments we show how the orbital decay of the SMBH closely follows analytical predictions when particle masses are significantly smaller than that of the SMBH. In a cosmological simulation of the assembly of a small galaxy, we show how our method allows for realistic black hole orbits. This approach overcomes the limitations of the advection scheme, where black holes are rapidly and artificially pushed toward the halo center and then forced to merge, regardless of their orbits. We find that SMBHs from merging dwarf galaxies can spend significant time away from the center of the remnant galaxy. Improving the modeling of SMBH orbital decay will help in making robust predictions of the growth, detectability, and merger rates of SMBHs, especially at low galaxy masses or at high redshift.