Parameters of Innermost Stable Circular Orbits of Spinning Test Particles: Numerical and Analytical Calculations

TL;DR

This paper investigates the innermost stable circular orbits (ISCO) of spinning test particles around Kerr black holes, providing numerical and analytical methods to determine ISCO parameters and their dependence on spins and black hole rotation.

Contribution

It offers new analytical calculations for small-spin corrections to ISCO parameters for arbitrary Kerr black hole spins, extending previous numerical results.

Findings

ISCO parameters depend on black hole and particle spins

Analytical small-spin corrections are derived for various Kerr black hole spins

The efficiency of accretion can exceed 42% with spinning test particles

Abstract

The motion of classical spinning test particles in the equatorial plane of a Kerr black hole is considered for the case where the particle spin is perpendicular to the equatorial plane. We review some results of our recent research of the innermost stable circular orbits (ISCO) [P.I. Jefremov, O.Yu. Tsupko and G.S. Bisnovatyi-Kogan, Phys.Rev. D 91 124030 (2015)] and present some new calculations. The ISCO radius, total angular momentum, energy, and orbital angular frequency are considered. We calculate the ISCO parameters numerically for different values of the Kerr parameter $a$ and investigate their dependence on both black hole and test particle spins. Then we describe in details how to calculate analytically small-spin corrections to the ISCO parameters for an arbitrary values of $a$. The cases of Schwarzschild, slowly rotating Kerr and extreme Kerr black hole are considered. The use of the orbital angular momentum is discussed. We also consider the ISCO binding energy. It is shown that the efficiency of accretion onto an extreme Kerr black hole can be larger than the maximum known efficiency (42 %) if the test body has a spin.