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.
