From Pericenter and Back: Full Debris Stream Evolution in Tidal Disruption Events

When a star passes too close to a supermassive black hole, it gets disrupted by strong tidal forces. The stellar debris then evolves into an elongated stream of gas that partly falls back toward the black hole. We present an analytical model describing for the first time the full stream evolution during such a tidal disruption event (TDE). Our framework consists of dividing the stream into different sections of elliptical geometry, whose properties are independently evolved in their comoving frame under the tidal, pressure, and self-gravity forces. Through an explicit treatment of the tidal force and the inclusion of the gas angular momentum, we can accurately follow the stream evolution near pericenter. Our model evolves the longitudinal stream stretching and both transverse widths simultaneously. For the latter, we identify two regimes depending on whether the dynamics is entirely dominated by the tidal force (ballistic regime) or additionally influenced by pressure and self-gravity (hydrostatic regime). We find that the stream undergoes transverse collapses both shortly after the stellar disruption and upon its return near the black hole, at specific locations determined by the regime of evolution considered. The stream evolution predicted by our model can be used to determine the subsequent interactions experienced by this gas that are at the origin of most of the electromagnetic emission from TDEs. Our results suggest that the accretion disk may be fed at a rate that differs from the standard fallback rate, which would provide novel observational signatures dependent on black hole spin.