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Soft X-ray Temperature Tidal Disruption Events from Stars on Deep Plunging Orbits

One of the puzzles associated with tidal disruption event candidates (TDEs) is that there is a dichotomy between the color temperatures of ${\rm few}\times 10^4$~K for TDEs discovered with optical and UV telescopes, and the color temperatures of ${\rm few}\times 10^5 - 10^6$~K for TDEs discovered with X-ray satellites. Here we propose that high-temperature TDEs are produced when the tidal debris of a disrupted star self-intersects relatively close to the supermassive black hole, in contrast to the more distant self-intersection that leads to lower color temperatures. In particular, we note from simple ballistic considerations that greater apsidal precession in an orbit is the key to closer self-intersection. Thus larger values of $β$, the ratio of the tidal radius to the pericenter distance of the initial orbit, are more likely to lead to higher temperatures of more compact disks which are super-Eddington and geometrically and optically thick. For a given star and $β$, apsidal precession also increases for larger black hole masses, but larger black hole masses imply a lower temperature at the Eddington luminosity. Thus the expected dependence of the temperature on the mass of the black hole is non-monotonic. We find that in order to produce a soft X-ray temperature TDE, a deep plunging stellar orbit with $β> 3$ is needed and a black hole mass of $\lesssim 5\times 10^6 M_\odot$ is favored. Although observations of TDEs are comparatively scarce and are likely dominated by selection effects, it is encouraging that both expectations are consistent with current data.