The Distribution of Inclinations of TDEs by Kerr Black Holes

A tidal disruption event (TDE) occurs when a star wanders close enough to a supermassive black hole (SBH) for its tidal fields to overwhelm the star’s self gravity. Some of the resulting stellar debris can be accreted by the SBH to power a bright electromagnetic flare that lasts from months to years. The orbital angular momentum of the tidally disrupted star will generally be inclined with respect to the SBH spin which may have several observational consequences for the resulting TDE including: (1) nodal precession of the tidal debris may delay its circularization and its accretion by the SBH, (2) Lense-Thirring of the accretion disk may lead to observable quasi-periodic oscillations, and (3) the inclination dependence of the energy of the innermost stable circular orbit (ISCO) affects the amount of energy available to power luminous emission. We calculate, as a function of SBH mass and spin, the distribution of TDE inclinations which results from a complicated interplay between spin-dependent tidal forces, the spin-dependent threshold for direct capture by the event horizon, and two-body relaxation that determines the stellar angular-momentum distribution. We find that the inclination distribution is biased towards prograde inclinations in the full loss-cone limit at low SBH masses, flips towards a retrograde bias at intermediate SBH masses and high binding energies where the stronger tidal forces on retrograde orbits dominate, and then returns to a strong prograde bias at higher masses where all retrograde orbits lead to direct capture.