  Tidal disruption events occur when a star is disrupted by a supermassive
black hole, resulting in an elongated stream of gas that partly falls back to
the pericenter. Due to apsidal precession, the returning stream may collide
with itself, leading to a self-crossing shock that launches an outflow. If the
black hole spins, this collision may additionally be affected by Lense-Thirring
precession that can cause an offset between the two stream components. We study
the impact of this effect on the outflow properties by carrying out local
simulations of collisions between offset streams. As the offset increases, we
find that the geometry of the outflow becomes less spherical and more
collimated along the directions of the incoming streams, with less gas getting
unbound by the interaction. However, even the most grazing collisions we
consider significantly affect the trajectories of the colliding gas, likely
promoting subsequent strong interactions near the black hole and rapid disc
formation. We analytically compute the dependence of the offset to stream width
ratio, finding that even slowly spinning black holes can cause both strong and
grazing collisions. We estimate that the self-crossing shock luminosity is
lower for an offset collision than an aligned one since radiation energy
injected by the shock is significantly lower for more offset collisions. We
find that the deviation from outflow sphericity may cause significant
variations in the efficiency at which X-ray radiation from the disc is
reprocessed to the optical band, depending on the viewing angle, and increase
the degree of the observed polarization. These potentially observable features
hold the promise of constraining the black hole spin from tidal disruption
events.
