Relativistic effects on tidal disruption kicks of solitary stars

Solitary stars that wander too close to their galactic centres can become tidally disrupted, if the tidal forces due to the supermassive black hole (SMBH) residing there overcome the self-gravity of the star. If the star is only partially disrupted, so that a fraction survives as a self-bound object, this remaining core will experience a net gain in specific orbital energy, which translates into a velocity "kick" of up to $\sim 10^3$ km/s. In this paper, we present the result of smoothed particle hydrodynamics (SPH) simulations of such partial disruptions, and analyse the velocity kick imparted on the surviving core. We compare $\gamma$ = 5/3 and $\gamma$ = 4/3 polytropes disrupted in both a Newtonian potential, and a generalized potential that reproduces most relativistic effects around a Schwarzschild black hole either exactly or to excellent precision. For the Newtonian case, we confirm the results of previous studies that the kick velocity of the surviving core is virtually independent of the ratio of the black hole to stellar mass, and is a function of the impact parameter $\beta$ alone, reaching at most the escape velocity of the original star. For a given $\beta$, relativistic effects become increasingly important for larger black hole masses. In particular, we find that the kick velocity increases with the black hole mass, making larger kicks more common than in the Newtonian case, as low-$\beta$ encounters are statistically more likely than high-$\beta$ encounters. The analysis of the tidal tensor for the generalized potential shows that our results are robust lower limits on the true relativistic kick velocities, and are generally in very good agreement with the exact results.