Capture Rates of Compact Objects by Supermassive Black Holes

Abstract

Capture rates of compact objects were calculated by using a recent solution of the Fokker-Planck equation in energy-space, including two-body resonant effects. The fraction of compact objects (white dwarfs, neutron stars and stellar black holes) was estimated as a function of the luminosity of the galaxy from a new grid of evolutionary models. Stellar mass densities at the influence radius of central supermassive black holes were derived from brightness profiles obtained by Hubble Space Telescope observations. The present study indicates that the capture rates scale as $\propto M_{bh}^{-1.048}$, consequence of the fact that dwarf galaxies have denser central regions than luminous objects. If the mass distribution of supermassive black holes has a lower cutoff at $\sim 1.4\times 10^6$ M$_{\odot}$ (corresponding to the lowest observed supermassive black hole mass, located in M32), then 9 inspiral events are expected to be seen by LISA (7-8 corresponding to white dwarf captures and 1-2 to neutron star and stellar black hole captures) after one year of operation. However, if the mass distribution extends down to $\sim 2\times 10^5$ M$_{\odot}$, then the total number of expected events increases up to 579 (corresponding to $\sim$ 274 stellar black hole captures, $\sim$ 194 neutron star captures and $\sim$ 111 white dwarf captures).