Energetic Explosions from Collisions of Stars at Relativistic Speeds in Galactic Nuclei
We consider collisions occurring between stars moving near the speed of light around supermassive black holes (SMBHs) with mass $M_{\bullet}\gtrsim10^8\,M_\odot$, without being tidally disrupted. In this SMBH range, for sun-like stars, the tidal-disruption radius is smaller than the SMBH's event horizon; therefore we do not expect to observe tidal disruption events. Differential collision rates are calculated by defining probability distribution functions for various parameters such as the impact parameter, distance from SMBH at time of collision, relative velocity between the two colliding stars, and the masses of the two colliding stars. The relative velocity parameter is drawn from a distribution function for SMBHs. We integrate over all parameters to arrive at a total collision rate for a galaxy with a specific SMBH mass. We then consider how the stellar population in the vicinity of the SMBH is depleted and replenished over time, and calculate the effect on the collision rate over time. We calculate the differential collision rate as a function of total energy released, energy released per unit mass lost, and galactocentric radius. The overall rate for collisions taking place in the inner $\sim1$ pc of galaxies with $M_{\bullet}=10^8,10^9,10^{10}\,M_\odot$ are $Γ\sim2.2\times10^{-3},2.2\times10^{-4},4.7\times10^{-5}$ yr$^{-1}$, respectively. The most common collisions release energies on the order of $\sim10^{49}-10^{51}$ erg, with the energy distribution peaking at higher energies in galaxies with more massive SMBHs. In addition, we show example light curves for collisions with varying parameters, and find that the peak luminosity could reach or even exceed that of superluminous supernovae. Weaker events could initially be mistaken for low-luminosity supernovae.