Gravothermal Collapse of Self-Interacting Dark Matter Halos and the Origin of Massive Black Holes

A central supermassive black hole (SMBH) with a mass $10^6-10^9 M_\odot$ appears to be a common feature in nearby galaxies and the likely power source in quasars and active galactic nuclei. We demonstrate that the formation of a central black hole is a natural and inevitable consequence of the gravothermal catastrophe in a self-interacting dark matter (SIDM) halo. Through gravothermal evolution driven by collisional relaxation, an SIDM halo will form a massive inner core whose density and velocity dispersion will increase secularly in time. Eventually, the inner core arrives at a relativistic radial instability and undergoes dynamical collapse to a black hole. The initial mass of the black hole will be $10^{-8}-10^{-6}$ of the total mass of the halo. We show that if at formation the overdensity in the SIDM halo is not too large, SMBHs in the observed mass range can form directly in very massive halos following core collapse. Alternatively, with large overdensities, moderate mass halos undergo core collapse to form central seed black holes of intermediate mass, and these holes can then merge and/or accrete to reach the SMBH range. Forming SMBHs by core collapse in SIDM halos requires no baryons, no prior epoch of star formation and no other mechanism of forming black holes seeds.