Energetic explosions from collisions of stars at relativistic speeds in galactic nuclei

¹ Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
² Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, Massachusetts 02138, USA
e-mail: aloeb@cfa.harvard.edu

Received: 9 April 2024
Accepted: 3 May 2024

Abstract

Aims. We investigated collisions that could occur between stars moving near the speed of light around supermassive black holes (SMBHs) with mass M_• ≳ 10⁸ M_⊙, without being tidally disrupted. Within this approximate SMBH mass range, for sun-like stars, the tidal-disruption radius is smaller than the SMBH’s event horizon; therefore we did not anticipate tidal disruption events (TDEs).

Methods. Differential collision rates were calculated by defining probability distribution functions for various parameters of interest, such as the impact parameter, distance from the SMBH at the time of the collision, the relative velocity between the two colliding stars, and the masses of the two colliding stars. The relative velocity parameter was drawn from an appropriate distribution function for SMBHs. We integrated over all these parameters to arrive at a total collision rate for a galaxy with a specific SMBH mass. We then considered how the stellar population in the vicinity of the SMBH was depleted and replenished over time, and calculated the effect this can have on the collision rate over time. We further calculated the differential collision rate as a function of the total energy released, the energy released per unit mass lost, and the galactocentric radius.

Results. The overall rate for collisions taking place within the inner ∼1 pc of galaxies with M_• = 10⁸, 10⁹, and 10¹⁰ M_⊙ are Γ ∼ 2.2 × 10⁻³, 2.2 × 10⁻⁴, and 4.7 × 10⁻⁵ yr⁻¹, respectively. The most common collisions would release energies on the order of ∼10⁴⁹ − 10⁵¹ ergs, with the energy distribution peaking at higher energies in galaxies with more massive SMBHs. In addition, we examined sample light curves for collisions with varying parameters, and find that the peak luminosity could reach or even exceed that of superluminous supernovae (SLSNe), albeit in the case of light curves with much shorter durations.

Conclusions. Weaker events may initially be mistaken for low-luminosity supernovae. In addition, we note that these events would likely create streams of debris that would accrete onto the SMBH, potentially creating accretion flares that may resemble TDEs.