A Cluster of Black Holes at the Galactic Center

If the stellar population of the bulge contains black holes formed in thefinal core collapse of ordinary stars with M \ga 30 M_{\odot}, then about25,000 stellar mass black holes should have migrated by dynamical friction intothe central parsec of the Milky Way, forming a black hole cluster around thecentral supermassive black hole. These black holes can be captured by thecentral black hole when they randomly reach a highly eccentric orbit due torelaxation, either by direct capture (when their Newtonian peribothron is lessthan 4 Schwarzschild radii), or after losing orbital energy throughgravitational waves. The overall depletion timescale is ~ 30 Gyr, so most ofthe 25,000 black holes remain in the central cluster today. The presence ofthis black hole cluster would have several observable consequences. First, thelow-mass, old stellar population should have been expelled from the regionoccupied by the black hole cluster due to relaxation, implying a core in theprofile of solar-mass red giants with a radius of ~ 2 pc (i.e., 1'). Theobserved central density cusp (which has a core radius of only a few arcseconds) should be composed primarily of young (\la 1 Gyr) stars. Second,flares from stars being captured by supermassive black holes in other galaxiesshould be rarer than usually expected because the older stars will have beenexpelled from the central regions by the black hole clusters of those galaxies.Third, the young (\la 2 Gyr) stars found at distances ~ 3 - 10 pc from theGalactic center should be preferentially on highly eccentric orbits. Fourth, iffuture high-resolution $K$-band images reveal sources microlensed by the MilkyWay's central black hole, then the cluster black holes could give rise tosecondary (``planet-like'') perturbations on the main event.Comment: submitted to Ap