  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 excitation. In the empty loss cone regime, where two-body
relaxation is weak, we estimate the number of consecutive partial disruptions
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.
