Dynamical Friction Modeling of Massive Black Holes in Cosmological
  Simulations and Effects on Merger Rate Predictions
  In this work we establish and test methods for implementing dynamical
friction for massive black hole pairs that form in large volume cosmological
hydrodynamical simulations which include galaxy formation and black hole
growth. We verify our models and parameters both for individual black hole
dynamics and for the black hole population in cosmological volumes. Using our
model of dynamical friction (DF) from collisionless particles, black holes can
effectively sink close to the galaxy center, provided that the black hole's
dynamical mass is at least twice that of the lowest mass resolution particles
in the simulation. Gas drag also plays a role in assisting the black holes'
orbital decay, but it is typically less effective than that from collisionless
particles, especially after the first billion years of the black hole's
evolution. DF from gas becomes less than $1\%$ of DF from collisionless
particles for BH masses $> 10^{7}$ M$_{\odot}$. Using our best DF model, we
calculate the merger rate down to $z=1.1$ using an $L_{\rm box}=35$ Mpc$/h$
simulation box. We predict $\sim 2$ mergers per year for $z>1.1$ peaking at
$z\sim 2$. These merger rates are within the range obtained in previous work
using similar-resolution hydro-dynamical simulations. We show that the rate is
enhanced by factor of $\sim 2$ when DF is taken into account in the simulations
compared to the no-DF run. This is due to $>40\%$ more black holes reaching the
center of their host halo when DF is added.
