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.
