Distribution of orbital inclinations for tidal disruption events by Kerr black holes

Abstract

The Kerr metric that describes the spacetime of a spinning supermassive black hole (SMBH) is axisymmetric, implying that the nearly parabolic geodesics on which stars approach the SMBH depend on the inclination angle $\iota$ of the orbital angular momentum with respect to the SMBH spin. This inclination affects both the geodesic deviation that determines whether a star is tidally disrupted and whether the tidal debris survives direct capture by the event horizon to produce an observable tidal disruption event (TDE). The steady-state TDE rate is the rate at which stars are scattered into the loss cone determined by these spin- and inclination-dependent effects. As the anisotropy of this loss-cone refilling is highly uncertain, we consider the two extreme limits in which stellar inclination is preserved (IP) or isotropized (ISO). We calculate the inclination distribution in these two limits and find a prograde bias in the IP limit because of the strong retrograde bias for direct capture. However, we find a retrograde bias in the ISO limit for intermediate SMBH masses when the empty loss cone suppresses capture and allows the weaker retrograde bias of geodesic deviation to dominate. Partially empty loss cones lead to steeper distributions of the penetration factor $\beta$ than for a full loss cone, with this effect even more pronounced in the ISO limit. We also calculate the total TDE rates and maximum SMBH mass $M_{\rm \bullet, max}$ for tidal disruption in these two limits. In the IP limit, we find a highly spin-dependent capture cutoff in the TDE rate and $M_{\rm \bullet, max} \approx 10^{8.45} M_\odot$ for maximal SMBH spin. In the ISO limit, we find a strong spin-dependent enhancement in the TDE rate at intermediate SMBH masses, a weakly spin-dependent capture cutoff above $M_\bullet \approx 10^{7.5} M_\odot$, and $M_{\rm \bullet, max} \approx 10^{7.95} M_\odot$ for maximal SMBH spin.