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

Zhong, Shiyan and Hayasaki, Kimitake and Li, Shuo and Berczik, Péter and Spurzem, Rainer (2020) Exploring the origin of stars on bound and unbound orbits causing tidal disruption events. ASTROPHYSICAL JOURNAL. ISSN 1538-4357

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Abstract

Tidal disruption events (TDEs) probe properties of supermassive black holes (SMBHs), their accretion disks, and the surrounding nuclear stellar cluster. Light curves of TDEs are related to orbital properties of stars falling SMBHs. We study the origin, density, and velocity distributions of bound and unbound stars in the nuclear star cluster, which are causing TDEs as a function of their orbital eccentricity $e$ and energy $E$. These quantities determine near the SMBH the ratio of the orbit's pericenter to tidal disruption radii (denoted as penetration factor, $\\beta$). We develop an analytical model for the density and velocity distribution of such stars in the cluster, which agrees well with N-body experiments. Our model extends classical models of angular momentum diffusion in the loss cone. We also derive an analytical model for three characteristic eccentricities in the loss cone: the minimum and maximum value for given $\\beta$, respectively, and $e_{\\rm lcb}$, which represents the orbital eccentricity defining the boundary between empty and full loss cone regimes. With N-body experiments, we show that stars causing TDEs are distributed between these eccentricity limits on the $e-\\beta$ plane. Moreover, we find most of the bound stars between $e_{\\rm lcb}$ and $e=1$ (i.e., the full loss cone regime), whereas the remaining bound stars are originating from the empty loss cone regime. This is consistent with the loss cone theory. We propose that the $e-\\beta$ distribution of stars in a star cluster or galactic nucleus can be a good tool to diagnose whether the stars can cause TDEs.

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