Ultra-deep tidal disruption events: Prompt self-intersections and observables

A star approaching a supermassive black hole (SMBH) can be torn apart in a tidal disruption event (TDE). We examine ultra-deep TDEs, a new regime in which the disrupted debris approaches close to the black hole's Schwarzschild radius, and the leading part intersects the trailing part at the first pericentre passage. We calculate the range of penetration factors β versus SMBH masses M that produce these prompt self-intersections using a Newtonian analytic estimate and a general relativistic (GR) geodesic model. We find that significant self-intersection of Solar-type stars requires β ∼ 50-127 for M/M☉ = 10⁴, down to β ∼ 5.6-5.9 for M/M☉ = 10⁶. We run smoothed particle hydrodynamic (SPH) simulations to corroborate our calculations and find close agreement, with a slightly shallower dependence on M. We predict that the shock from the collision emits an X-ray flare lasting t ∼ 2 s with L ∼ 10⁴⁷ erg s⁻¹ at E ∼ 2 keV, and the debris has a prompt accretion episode lasting t ∼ several minutes. The events are rare and occur with a rate N ≲ 10⁻⁷ Mpc⁻³ yr⁻¹. Ultra-deep TDEs can probe the strong gravity and demographics of low-mass SMBHs.