Converged simulations of the nozzle shock in tidal disruption events

Abstract: When debris from a star that experienced a tidal disruption events (TDE) after passing too close to a massive black hole returns to pericenter on the second passage, it is compressed, leading to the formation of nozzle shocks (in the orbital plane) and pancake shocks (perpendicular to the orbital plane). Resolving these shocks is a long-standing problem in the hydrodynamic simulations of parabolic TDEs. Excessive numerical energy dissipation or heating unrealistically expands the stream. In this Letter, we apply adaptive particle refinement to our 3D general relativistic smoothed particle simulations to locally increase the resolution near the pericenter. We achieve resolutions equivalent to $6.55\times10<sup>{11}$ particles, allowing us to converge on the true energy dissipation. We conclude that only $4\times10<sup>{-5}$ of the orbital energy is dissipated in nozzle shocks for a Sun-like star tidally disrupted by a $10^6$ solar-mass black hole, therefore the nozzle shocks are unlikely to be important in the evolution of TDEs.