Title:
Ultra-deep tidal disruption events: prompt self-intersections and observables

Abstract:
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 t
he first pericentre passage. We calculate the range of penetration factors beta 
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 beta ~ 50-127 for 
M/M_{Sun} = 10^4, down to beta ~ 5.6-5.9 for M/M_{Sun} = 10^6. 
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 ~ 10^{47} 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.