Formation of Massive Black Holes in Galactic Nuclei: Runaway Tidal Encounters

Nuclear star clusters (NSCs) and supermassive black holes (SMBHs) both inhabit galactic nuclei, coexisting in a range of bulge masses, but excluding each other in the largest or smallest galaxies. We propose that the transformation of NSCs into SMBHs occurs via runaway tidal captures, once NSCs exceed a certain critical central density and velocity dispersion. The bottleneck in this process, as with all collisional runaways, is growing the first e-fold in black hole mass. The growth of a stellar mass black hole past this bottleneck occurs as tidally captured stars are consumed in repeated episodes of mass transfer at pericenter. Tidal captures may turn off as a growth channel once the black hole reaches a mass ~100-1000 solar masses, but tidal disruption events will continue and appear capable of growing the seed SMBH to larger sizes. The runaway slows (becomes sub-exponential) once the seed SMBH consumes the core of its host NSC. While the bulk of the cosmic mass density in SMBHs is ultimately produced (via the Soltan-Paczynski argument) by episodic gaseous accretion in very massive galaxies, the smallest SMBHs have probably grown from strong tidal encounters with NSC stars. SMBH seeds that grow for a time $t$ entirely through this channel will follow simple power law relations with the velocity dispersion, $\sigma$, of their host galaxy. In the simplest regime it is $M_\bullet \sim \sigma^{3/2}\sqrt{M_\star t / G} \sim 10^{6}M_\odot (\sigma / 50~{\rm km~s}^{-1})^{3/2}(t/10^{10}~{\rm yr})^{1/2}$, but the exponents and prefactor can differ slightly depending on the details of loss cone refilling. Current tidal disruption event rates predicted from this mechanism are consistent with observations.