Stars Crushed by Black Holes. I. On the Energy Distribution of Stellar Debris in Tidal Disruption Events

The distribution of orbital energies imparted into stellar debris following the close encounter of a star with a supermassive black hole is the principal factor in determining the rate of return of debris to the black hole, and thus in determining the properties of the resulting lightcurves from such events. We present simulations of tidal disruption events for a range of $\beta\equiv r_{\rm t}/r_{\rm p}$ where $r_{\rm p}$ is the pericentre distance and $r_{\rm t}$ the tidal radius. We perform these simulations at different spatial resolutions to determine the numerical convergence of our models. We compare simulations in which the heating due to shocks is included or excluded from the dynamics. For $\beta \lesssim 8$ the simulation results are well-converged at sufficiently moderate-to-high spatial resolution, while for $\beta \gtrsim 8$ the breadth of the energy distribution can be grossly exaggerated by insufficient spatial resolution. We find that shock heating plays a non-negligible role only for $\beta \gtrsim 4$, and that typically the effect of shock heating is mild. We show that self-gravity can modify the energy distribution over time after the debris has receded to large distances for all $\beta$. Primarily, our results show that across a range of impact parameters, while the shape of the energy distribution varies with $\beta$, the width of the energy spread imparted to the bulk of the debris is closely matched to the canonical spread, $\Delta E = GM_\bullet R_\star/r_{\rm t}^2$, for the range of $\beta$ we have simulated.