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 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 pericentre. Tidal captures may deactivate as a growth channel once the black hole mass greater than or similar to 10(2-3)M(circle dot), but tidal disruption events will continue and can grow the seed SMBH to larger sizes. The runaway slows (becomes subexponential) once the seed SMBH consumes the core of its host NSC. While most of the cosmic mass density in SMBHs is ultimately produced 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 powerlaw relations with the velocity dispersion, sigma, of their host galaxy. In the simplest regime, it is M. similar to sigma(3/2)root M.t/G similar to 10(6)M circle dot(sigma/ 50 km s(-1))(3/2)(t/ 10(10) 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.