The effect of impact parameter on tidal disruption events

Stars that pass too close to a supermassive black hole are disrupted by the black hole's tidal gravity and leads to some debris being ejected while the remainder accretes into the black hole. To better study the physics of this debris, we use the moving mesh code MANGA to follow the evolution of the star from its initial encounter to its complete destruction. By varying the impact parameter ($\beta$) of the star, we studied the energy distribution of the remaining material and the fallback rate of the material into the black hole as a function of time. We show that the spread of energy in the debris and peak luminosity time ($t_{\rm peak}$) are both directly related to the impact parameter. In particular, we find a $\beta^{1/2}$ scaling for the energy spread for $\beta=2-10$ and a frozen evolution for $\beta\gtrsim 10$. We provide analytic arguments for the spread of energy, rise time of the light curve, and broadness of the luminosity peak for these lower $\beta$'s. These relationships provide a possible means of inferring the impact parameters for observed TDEs.