# Partial Stellar Disruption by a Supermassive Black Hole: Is the Lightcurve Really Proportional to $t^{-9/4}$?

## TL;DR

This paper models partial stellar disruptions by supermassive black holes, revealing that the fallback rate scales as t^{-2.26} and challenging previous assumptions about TDE lightcurve decay rates.

## Contribution

It introduces a new model for partial TDEs with a surviving stellar core, showing the fallback rate scales as t^{-2.26} and differs from the classical t^{-5/3} and t^{-9/4} decay laws.

## Key findings

- Fallback rate scales as t^{-2.26} in partial TDEs.
- Late-time accretion declines as t^{-5/3} or t^{-9/4} depending on disruption completeness.
- Previous models assuming Keplerian orbits overlooked this new scaling.

## Abstract

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 $\propto t^{-2.26\pm0.01}$, 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recovered this result due to the assumption of a Keplerian energy-period relationship for the debris orbits, which is no longer valid when a surviving core generates a time-dependent, gravitational potential.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.