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 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. 
Eric R. Coughlin, Chris Nixon, Mitchell C. Begelman, Philip J.   Armitage
astro-ph.HE