Understanding black hole mass assembly via accretion and mergers at late
  times in cosmological simulations
  Accretion is thought to primarily contribute to the mass accumulation history
of supermassive black holes throughout cosmic time. While this may be true at
high redshifts, at lower redshifts and for the most massive black holes mergers
themselves might add significantly to the mass budget. We evolve SMBHs from $4
> z > 0$ using merger trees derived from hydrodynamical cosmological
simulations of a cluster and void region, scaled to the observed value of the
stellar mass fraction to account for overcooling. Mass gains from gas accretion
proportional to bulge growth and BH-BH mergers are tracked, as are black holes
that remain "orbiting" due to insufficient dynamical friction in a merger
remnant, as well as those that are ejected due to gravitational recoil. We find
that gas accretion remains the dominant source of mass accumulation in almost
all SMBHs; mergers contribute $2.5\pm0.1\%$ for all SMBHs in the cluster and
$1.0\pm0.1\%$ in the void since $z = 4$. However, mergers are significant for
massive SMBHs. The fraction of mass accumulated from mergers for central BHs
generally increases for larger values of the host bulge mass: in the void, the
fraction is $2\%$ at $M_{*, bul} = 10^{10} M_{\odot}$, increasing to $4\%$ at
$M_{*, bul} \gtrsim 10^{11} M_{\odot}$, and in the cluster it is $4\%$ at
$M_{*, bul} = 10^{10} M_{\odot}$ and $23\%$ at $10^{12} M_{\odot}$. We find
that $40\%$ of SMBHs and $\approx 8\%$ of the total SMBH mass is found orbiting
in the cluster region at $z = 0$. The existence of orbiting and ejected SMBHs
requires modification of the Soltan argument. We estimate this correction to
the integrated accreted mass density of SMBHs to be in the range $6-21\%$, with
a mean value of $11\pm3\%$. We also calculate the total energy output and
strain from gravitational waves emitted by merging SMBHs, and obtain a signal
potentially detectable by pulsar timing arrays.
