Innermost stable circular orbits around relativistic rotating stars

Details Innermost stable circular orbits around relativistic rotating stars Innermost stable circular orbits around relativistic rotating stars

1998-07-17

arxiv.org/abs/gr-qc/9807046v1

Phys.Rev.D58:104011,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 2 figures, accepted for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.58.104011

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.

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