Collision of an innermost stable circular orbit particle around a Kerr black hole

Tomohiro Harada; Masashi Kimura

doi:10.1103/PhysRevD.83.024002

paper

Collision of an innermost stable circular orbit particle around a Kerr black hole

arXiv:1010.0962 · doi:10.1103/PhysRevD.83.024002

Abstract

We derive a general formula for the center-of-mass (CM) energy for the near-horizon collision of two particles of the same rest mass on the equatorial plane around a Kerr black hole. We then apply this formula to a particle which plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. It is found that the maximum value of the CM energy $E_{cm}$ is given by $E_{cm} / (2 m_{0}) ≃ 1.40/ 4 1 - a_{*}^{2}$ for a nearly maximally rotating black hole, where $m_{0}$ is the rest mass of each particle and $a_{*}$ is the nondimensional Kerr parameter. This coincides with the known upper bound for a particle which begins at rest at infinity within a factor of 2. Moreover, we also consider the collision of a particle orbiting the ISCO with another particle on the ISCO and find that the maximum CM energy is then given by $E_{cm} / (2 m_{0}) ≃ 1.77/ 6 1 - a_{*}^{2}$ . In view of the astrophysical significance of the ISCO, this result implies that particles can collide around a rotating black hole with an arbitrarily high CM energy without any artificial fine-tuning in an astrophysical context if we can take the maximal limit of the black hole spin or $a_{*} \to 1$ . On the other hand, even if we take Thorne's bound on the spin parameter into account, highly or moderately relativistic collisions are expected to occur quite naturally, for $E_{cm} / (2 m_{0})$ takes 6.95 (maximum) and 3.86 (generic) near the horizon and 4.11 (maximum) and 2.43 (generic) on the ISCO for $a_{*} = 0.998$ . This implies that high-velocity collisions of compact objects are naturally expected around a rapidly rotating supermassive black hole. Implications to accretion flows onto a rapidly rotating black hole are also discussed.

24 pages, 2 figures, accepted for publication in Physical Review D, minor correction

Collision of an innermost stable circular orbit particle around a Kerr black hole

Abstract

References in corpus (7)

Cited by in corpus (86)