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Tidal disruption events (TDEs) provide a clue to the properties of a centralsupermassive black hole (SMBH) and an accretion disk around it, and to thestellar density and velocity distributions in the nuclear star clustersurrounding the SMBH. Deviations of TDE light curves from the standardoccurring at a parabolic encounter with the SMBH depends on whether the stellarorbit is hyperbolic or eccentric (Hayasaki et al. 2018) and the penetrationfactor ($\beta$, tidal disruption radius to orbital pericenter ratio). We studythe orbital parameters of bound and unbound stars being tidally disrupted bycomparison of direct $N$-body simulation data with an analytical model.Starting from the classical steady-state Fokker-Planck model of Cohn & Kulsrud(1978), we develop an analytical model of the number density distribution ofthose stars as a function of orbital eccentricity ($e$) and $\beta$. To do sofittings of the density and velocity distribution of the nuclear star clusterand of the energy distribution of tidally disrupted stars are required andobtained from $N$-body data. We confirm that most of the stars causing TDEs ina spherical nuclear star cluster originate from the full loss-cone region ofphase space, derive analytical boundaries in eccentricity-$\beta$ space, andfind them confirmed by $N$-body data. Since our limiting eccentricities aremuch smaller than critical eccentricities for full accretion or full escape ofstellar debris, we conclude that those stars are only very marginally eccentricor hyperbolic, close to parabolic.

Exploring the origin of stars on bound and unbound orbits causing tidal disruption events