Thawing the frozen-in approximation: implications for self-gravity in deeply plunging tidal disruption events

The tidal destruction of a star by a massive black hole, known as a tidal disruption event (TDE), is commonly modelled using the `frozen-in' approximation. Under this approximation, the star maintains exact hydrostatic balance prior to entering the tidal sphere (radius r_t), after which point its internal pressure and self-gravity become instantaneously negligible and the debris undergoes ballistic free fall. We present a suite of hydrodynamical simulations of TDEs with high penetration factors β ≡ r_t/r_p = 5-7, where r_p is the pericentre of the stellar centre of mass, calculated using a Voronoi-based moving-mesh technique. We show that basic assumptions of the frozen-in model, such as the neglect of self-gravity inside r_t, are violated. Indeed, roughly equal fractions of the final energy spread accumulate exiting and entering the tidal sphere, though the frozen-in prediction is correct at the order-of-magnitude level. We also show that an O(1) fraction of the debris mass remains transversely confined by self-gravity even for large β which has implications for the radio emission from the unbound debris and, potentially, for the circularization efficiency of the bound streams.