Orbital In-spiral into a Massive Black Hole in a Galactic Center

A massive black hole (MBH) in a galactic center drives a flow of stars into nearly radial orbits to replace those it destroyed. Stars whose orbits cross the event horizon r_S or the tidal disruption radius r_t are promptly destroyed in an orbital period P. Stars with orbital periapse r_p slightly larger than the sink radius q ≡ max(r_S, r_t) may slowly spiral in as a result of dissipative interactions with the MBH, e.g., gravitational wave emission, tidal heating, or accretion disk drag, with observable consequences and implications for the MBH growth rate. Unlike prompt destruction, the in-spiral time is typically ≫P. This time is limited by the same scattering process that initially deflected the star into its eccentric orbit, since it can deflect it again to a wider orbit where dissipation is inefficient. The ratio between slow and prompt event rates is therefore much smaller than that implied by the ratio of cross sections, ~r_p/q, and so only prompt disruption contributes significantly to the mass of the MBH. Conversely, most stars that scatter off the MBH survive the extreme tidal interaction ("tidal scattering"). We derive general expressions for the in-spiral event rate and the mean number of in-spiraling stars, and we show that the survival probability of tidally scattered stars is ~1 and that the number of tidally heated stars ("squeezars") and gravity-wave-emitting stars in the galactic center is ~0.1-1.