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

Tomohiro Harada and Masashi Kimura
Phys. Rev. D 83, 024002 – Published 4 January 2011

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 Ecm is given by Ecm/(2m0)1.40/1a*24 for a nearly maximally rotating black hole, where m0 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 Ecm/(2m0)1.77/1a*26. 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*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 Ecm/(2m0) 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.

  • Figure
  • Figure
  • Received 8 September 2010

DOI:https://doi.org/10.1103/PhysRevD.83.024002

© 2011 The American Physical Society

Authors & Affiliations

Tomohiro Harada1,* and Masashi Kimura2,†

  • 1Department of Physics, Rikkyo University, Toshima, Tokyo 175-8501, Japan
  • 2Department of Mathematics and Physics, Graduate School of Science, Osaka City University, Osaka 558-8585, Japan

  • *harada@rikkyo.ac.jp
  • mkimura@sci.osaka-cu.ac.jp

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 83, Iss. 2 — 15 January 2011

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×