Partial Stellar Disruption by a Supermassive Black Hole: Is the Light Curve Really Proportional to t ^-9/4?

The tidal disruption of a star by a supermassive black hole, and the subsequent accretion of the disrupted debris by that black hole, offers a direct means to study the inner regions of otherwise-quiescent galaxies. These tidal disruption events (TDEs) are being discovered at an ever-increasing rate. We present a model for the evolution of the tidally disrupted debris from a partial TDE, in which a stellar core survives the initial tidal encounter and continues to exert a gravitational influence on the expanding stream of tidally stripped debris. We use this model to show that the asymptotic fallback rate of material to the black hole in a partial TDE scales as ∝ t ^-2.26±0.01, and is effectively independent of the mass of the core that survives the encounter; we also estimate the rate at which TDEs approach this asymptotic scaling as a function of the core mass. These findings suggest that the late-time accretion rate onto a black hole from a TDE either declines as t ^-5/3 if the star is completely disrupted or t ^-9/4 if a core is left behind. We emphasize that previous investigations have not recovered this result due to the assumption of a Keplerian energy-period relationship for the debris orbits, which is no longer valid when a surviving core generates a time-dependent, gravitational potential. This dichotomy of fallback rates has important implications for the characteristic signatures of TDEs in the current era of wide-field surveys.