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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.