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 explore this in two disparate environments — a massive cluster and a void region .
We evolve SMBHs from 4 > z > 0 using merger trees derived from hydrodynamical cosmological simulations of these two regions , 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 \pm 0.1 \% for all SMBHs in the cluster and 1.0 \pm 0.1 \% in the void since z = 4 .
However , mergers are significant for massive SMBHs .
The fraction of mass accumulated from mergers for central black holes generally increases for larger values of the host bulge mass : in the void , the fraction is 2 \% at M _ { *, \mathrm { bul } } = 10 ^ { 10 } M _ { \odot } , increasing to 4 \% at M _ { *, \mathrm { bul } } \gtrsim 10 ^ { 11 } M _ { \odot } , and in the cluster it is 4 \% at M _ { *, \mathrm { bul } } = 10 ^ { 10 } M _ { \odot } and 23 \% at 10 ^ { 12 } M _ { \odot } .
We also find that the total mass in orbiting SMBHs is negligible in the void , but significant in the cluster , in which a potentially detectable 40 \% of SMBHs and \approx 8 \% of the total SMBH mass where the total includes central , orbiting , and ejected SMBHs is found orbiting 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 \pm 3 \% .
Quantifying the growth due to mergers at these late times , we calculate the total energy output and strain from gravitational waves emitted by merging SMBHs , and obtain a signal potentially detectable by pulsar timing arrays .