On the structure of tidally disrupted stellar debris streams

A tidal disruption event (TDE) - when a star is destroyed by the immense gravitational field of a supermassive black hole - transforms a star into a stream of tidally shredded debris. The properties of this debris ultimately determine the observable signatures of tidal disruption events (TDEs). Here we derive a simple, self-similar solution for the velocity profile of the debris streams produced from TDEs, and show that this solution agrees extremely well with numerical results. Using this self-similar solution, we calculate an analytic, approximate expression for the radial density profile of the stream. We show that there is a critical adiabatic index that varies as a function of position along the stream above (below) which the stream is unstable (stable) to gravitational fragmentation. We also calculate the impact of heating and cooling on this stability criterion.