Approximate analytic light curves for the tidal disruption of a polytropic star

Abstract

Tidal disruption events are characterized by an X-ray flare whose luminosity falls off as t^-5/3 at late times. Modelling the disruption process is usually done numerically, but it is computationally expensive. In this paper, we derive approximate analytic light curves for polytropic stars disrupted by a supermassive black hole to get more insights on the physics of the disruption. We compared this with numerical results using the same model and the overall shape of the light curves was the same. With the analytic expression, we get the n-dependence of the light curve where the general form falls off with the same proportionality as the canonical fallback rate, independent of the value of the polytropic index n.