Tidal disruption of a star in the Schwarzschild spacetime: relativistic effects in the return rate of debris

Abstract

Motivated by an improved multi-wavelength observational coverage of the transient sky, we investigate the importance of relativistic effects in disruptions of stars by non-spinning black holes (BHs). This paper focuses on calculating the ballistic rate of return of debris to the black hole as this rate is commonly assumed to be proportional to the light curve of the event. We simulate the disruption of a low mass main sequence star by BHs of varying masses ($10^5,10^6,10^7 M_\odot$) and of a white dwarf by a $10^5 M_\odot$ BH. Based on the orbital energy as well as angular momentum of the debris, we infer the orbital distribution and estimate the return rate of the debris following the disruption. We find two signatures of relativistic disruptions: a gradual rise as well as a delayed peak in the return rate curves relative to their Newtonian analogs. Assuming that the return rates are proportional to the light curves, we find that relativistic effects are in principle measurable given the cadence and sensitivity of the current transient sky surveys. Accordingly, using a simple model of a relativistic encounter with a Newtonian parametric fit of the peak leads to an overestimate in the BH mass by a factor of $\sim {\rm few}\times0.1$ and $\sim {\rm few}$ in the case of the main sequence star and white dwarf tidal disruptions, respectively.