Innermost stable circular orbits around magnetized rotating massive stars

TL;DR

This paper extends existing formulas for the innermost stable circular orbit (ISCO) around rotating stars by including magnetic effects, providing accurate approximations validated against exact solutions and numerical data, with implications for neutron star modeling.

Contribution

The paper introduces a generalized analytical formula for ISCO radius around magnetized rotating stars, incorporating magnetic dipole moments and validating its accuracy.

Findings

ISCO radius decreases with increasing magnetic field.

For magnetic fields below 100GT, the non-magnetized approximation remains valid.

Derived analytical formulas for particle angular velocity, energy, and angular momentum at ISCO.

Abstract

In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating and deformed source. In the present paper, we generalize their expression by including the magnetic dipole moment. We show that our approximate analytical formulas are accurate enough by comparing them with the six-parametric exact solution calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with increasing magnetic field. However, for magnetic fields below 100GT the variation of the radius at ISCO is negligible and hence the non-magnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy and angular momentum of the test particle at ISCO.