Innermost stable circular orbits around relativistic rotating stars

TL;DR

This paper derives and validates approximate formulas for the innermost stable circular orbit (ISCO) around rotating relativistic stars, highlighting the significance of mass quadrupole moments in such calculations.

Contribution

It introduces new analytic formulas for ISCO parameters around rotating stars, incorporating higher multipole moments and validating them against numerical models.

Findings

Analytic formulas closely match numerical results.

Mass quadrupole moment significantly affects ISCO properties.

Rotation and multipole moments are crucial for accurate ISCO determination.

Abstract

We investigate the innermost stable circular orbit (ISCO) of a test particle moving on the equatorial plane around rotating relativistic stars such as neutron stars. First, we derive approximate analytic formulas for the angular velocity and circumferential radius at the ISCO making use of an approximate relativistic solution which is characterized by arbitrary mass, spin, mass quadrupole, current octapole and mass $2^4$-pole moments. Then, we show that the analytic formulas are accurate enough by comparing them with numerical results, which are obtained by analyzing the vacuum exterior around numerically computed geometries for rotating stars of polytropic equation of state. We demonstrate that contribution of mass quadrupole moment for determining the angular velocity and, in particular, the circumferential radius at the ISCO around a rapidly rotating star is as important as that of spin.