Repeated Tidal Interactions Between Stars and Supermassive Black Holes: Mass Transfer, Stability, and Implications for Repeating Partial Tidal Disruption Events

Stars orbiting supermassive black holes can generate recurring accretion flares in repeating partial tidal disruption events (TDEs). Here, we develop an efficient formalism for analyzing the time-dependent response of a star to the removal of a fraction (less than or similar to 10%) of its mass. This model predicts that mass loss results in a decrease in the average density of low-mass (less than or similar to 0.7M circle dot) stars. In contrast, higher-mass stars exhibit an increase in their average density, such that the change is more pronounced for larger mass losses, and stars with masses similar to 1.5-2M circle dot experience the largest such increase. We predict that the final energy of the star post-mass-loss (i.e., the "surviving core") is effectively given by the binding energy of the original star interior to the radius from which mass is removed, i.e., the final core energy is agnostic to the process that removes the mass and-as a corollary-tidal heating is comparatively insignificant. We find excellent agreement between our predictions and one-dimensional Eulerian simulations of a star undergoing mass loss, and three-dimensional Lagrangian simulations of partial TDEs. We conclude that (1) partially disrupted stars are not significantly heated via tidal dissipation, (2) evolved and moderately massive (greater than or similar to 1.5M circle dot) stars can most readily survive many repeated stripping events, and (3) progressively dimmer flares-observed in some repeating partial TDE candidates-could be explained by the increase in the density of the star post-mass-loss.