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Capture of stellar--mass compact objects by massive black holes in galactic cusps

A significant fraction of the stellar population in the cusp around central black holes of galaxies consists of compact remnants of evolved stars, such as white dwarfs, neutron stars and stellar mass black holes. We estimate the rate of capture of compact objects by massive central black holes, assuming most spiral galaxies have a central black hole of modest mass ($\sim 10^6 \msun$), and a cuspy spheroid. It is likely that the total capture rate is dominated by nucleated spirals. We estimate the flux of gravitational wave radiation from such coalescences, and the estimated detectable source count for proposed space--based gravitational wave observatories such as LISA. About one event per year should be detectable within $1 \, {\rm Gpc}$, given very conservative estimates of the black hole masses and central galactic densities. We expect $10^2$--$10^3$ detectable sources at lower frequencies ($10^{-4}$ Hz) ``en route'' to capture. If stellar mass black holes are ubiquitous, the signal may be dominated by stellar mass black holes coalescing with massive black holes. The rate of white dwarf--white dwarf mergers in the cores of nucleated spirals is estimated at $\sim10^{-6}$ per year per galaxy.