Stream Crossing in Tidal Disruption Events

In a tidal disruption event (TDE), a star approaching a black hole is torn apart by the black hole's tidal force, resulting in the squeezing of the star to form a stream of tidally disrupted material (both bound and unbound). To understand the outcome of TDEs, it is crucial to find where the bound stream intersects itself since intersection can lead to potentially observable shocks, accretion disks and secondary outflows. We compute the intersection regions for a Schwarzschild (non-spinning) black hole and a Kerr (spinning) black hole. We numerically integrate the geodesic equations of motion to find the path of the stream and discuss the algorithm used to find the region of self-intersection. This algorithm takes into account various aspects of the model including stream thickness and energy distribution of the stream material. As a result, we obtain the dependence of the self-intersection region on multiple parameters such as inclination, energy, angular momentum and black hole spin. We also present a novel model for the stream thickness evolution that takes into account general relativistic corrections, and as a result find that shocks do not necessarily happen at the pericenter or the apocenter.