Self-intersection of the fallback stream in tidal disruption events

We propose a semi-analytical model for the self-intersection of the fallback stream in tidal disruption events (TDEs). When the initial periapsis is less than about 15 gravitational radii, a large fraction of the shocked gas is unbound in the form of a collision-induced outflow (CIO). This is because large apsidal precession causes the stream to self-intersect near the local escape speed at radius much below the apocentre. The rest of the fallback gas is left in more tightly bound orbits and quickly joins the accretion flow. We propose that the CIO is responsible for reprocessing the hard emission from the accretion flow into the optical band. This picture naturally explains the large photospheric radius [or low blackbody (BB) temperature] and typical line widths for optical TDEs. We predict the CIO-reprocessed spectrum in the infrared to be L_ν ∝ ν^∼0.5, shallower than a BB. The partial sky coverage of the CIO also provides a unification of the diverse X-ray behaviours of optical TDEs. According to this picture, optical surveys filter out a large fraction of TDEs with low-mass blackholes due to lack of a reprocessing layer, and the volumetric rate of optical TDEs is nearly flat wrt. the blackhole mass in the range M≲ 10^7 M_{⊙}. This filtering also causes the optical TDE rate to be lower than the total rate by a factor of ∼10 or more. When the CIO is decelerated by the ambient medium, radio emission at the level of that in ASASSN-14li is produced, but the time-scales and peak luminosities can be highly diverse. Finally, our method paves the way for global simulations of the disc formation process by injecting gas at the intersection point according to the prescribed velocity and density profiles.