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 holes Schwarzschild radius, and the leading part intersects the trailing part at the first pericenter passage. We calculate the range of penetration factors $beta$ vs 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 $beta sim 50 - 127$ for $M/M_odot = 10^4$, down to $beta sim 5.6 - 5.9$ for $M/M_odot = 10^6$. 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 $t sim 2$ s with $L sim 10^{47}$ ergs/s at $E sim 2$ keV, and the debris has a prompt accretion episode lasting $t sim$ several min. The events are rare and occur with a rate $dot{N} lesssim 10^{-7}$ Mpc$^{-3}$ yr$^{-1}$. Ultra-deep TDEs can probe the strong gravity and demographics of low-mass SMBHs.
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