  A tidal disruption event, which occurs when a star is destroyed by the
gravitational field of a supermassive black hole, produces a stream of debris,
the evolution of which ultimately determines the observational properties of
the event. Here we show that a post-periapsis caustic -- a location where the
locus of gas parcels comprising the stream would collapse into a
two-dimensional surface if they evolved solely in the gravitational field of
the hole -- occurs when the pericenter distance of the star is on the order of
the tidal radius of the hole. It is demonstrated that this "pancake" induces
significant density perturbations in the debris stream, and, for stiffer
equations of state (adiabatic index $\gamma \gtrsim 5/3$), these fluctuations
are sufficient to gravitationally destabilize the stream, resulting in its
fragmentation into bound clumps. The results of our findings are discussed in
the context of the observational properties of tidal disruption events.

High Energy Astrophysical Phenomena