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Disc formation from tidal disruptions of stars on eccentric orbits by Schwarzschild black holes

The potential of tidal disruption of stars to probe otherwise quiescent supermassive black holes cannot be exploited, if their dynamics is not fully understood. So far, the observational appearance of these events has been derived from analytical extrapolations of the debris dynamical properties just after disruption. By means of hydrodynamical simulations, we investigate the subsequent fallback of the stream of debris towards the black hole for stars already bound to the black hole on eccentric orbits. We demonstrate that the debris circularize due to relativistic apsidal precession which causes the stream to self-cross. The circularization timescale varies between 1 and 10 times the period of the star, being shorter for more eccentric and/or deeper encounters. This self-crossing leads to the formation of shocks that increase the thermal energy of the debris. If this thermal energy is efficiently radiated away, the debris settle in a narrow ring at the circularization radius with shock-induced luminosities of $\sim 10-10^3 \, L_{\rm Edd}$. If instead cooling is impeded, the debris form an extended torus located between the circularization radius and the semi-major axis of the star with heating rates $\sim 1-10^2 \, L_{\rm Edd}$. Extrapolating our results to parabolic orbits, we infer that circularization would occur via the same mechanism in $\sim 1$ period of the most bound debris for deeply penetrating encounters to $\sim 10$ for grazing ones. We also anticipate the same effect of the cooling efficiency on the structure of the disc with associated luminosities of $\sim 1-10 \, L_{\rm Edd}$ and heating rates of $\sim 0.1-1 \, L_{\rm Edd}$. In the latter case of inefficient cooling, we deduce a viscous timescale generally shorter than the circularization timescale. This suggests an accretion rate through the disc tracing the fallback rate, if viscosity starts acting promptly.