Repeating partial disruptions and two-body relaxation

Two-body relaxation may drive stars onto near-radial orbits around a massive black hole, resulting in a tidal disruption event (TDE). In some circumstances, stars are unlikely to undergo a single terminal disruption, but rather to have a sequence of many grazing encounters with the black hole. It has long been unclear what is the physical outcome of this sequence: each of these encounters can only liberate a small amount of stellar mass, but may significantly alter the orbit of the star. We study the phenomenon of repeating partial tidal disruptions (pTDEs) by building a semi-analytical model that accounts for mass loss and tidal excitations. In the empty loss cone regime, where two-body relaxation is weak, we estimate the number of consecutive partial disruption that a star can undergo, on average, before being significantly affected by two-body encounters. We find that in this empty loss cone regime, a star will be destroyed in a sequence of weak pTDEs, possibly explaining the tension between the low observed TDE rate and its higher theoretical estimates.