Universal relations for innermost stable circular orbits around rapidly rotating neutron stars

TL;DR

This paper derives universal, EOS-insensitive relations for the ISCO around rapidly rotating neutron stars, enabling mass estimation from observed QPOs without slow rotation assumptions.

Contribution

It introduces two nearly EOS-insensitive relations connecting ISCO radius and frequency to neutron star mass and spin, applicable to accreting neutron stars.

Findings

Universal relations are accurate within 2% for a wide range of parameters.

The ISCO radius relation matches Kerr black hole predictions within 6%.

Mass of neutron star in 4U 0614+09 estimated at 2.0 solar masses.

Abstract

We study the innermost stable circular orbit (ISCO) of a test particle around rapidly rotating neutron stars. Based on 12 different nuclear-matter equations of state (EOS), we find numerically two approximately EOS-insensitive universal relations that connect the radius and orbital frequency of the ISCO to the spin frequency $f$ and mass $M$ of rotating neutron stars. The relations are EOS-insensitive to about the 2% level for a large range of $Mf$. We also find that the universal relation for the ISCO radius agrees with the corresponding relation for the Kerr black hole to within 6% up to $Mf=5000 M_\odot {\rm Hz}$. Our relations can be applied to accreting neutron stars in low-mass X-ray binaries. Using the spin frequency $f=414$ Hz and the highest kilohertz quasi-periodic oscillations (kHz QPOs) at 1220 Hz observed in the system 4U 0614+09, we determine the mass of the neutron star to be $2.0 M_\odot$. Our conclusion only makes a minimal assumption that the highest kHz QPO frequency is the ISCO frequency, bypassing the assumption of slow rotation and the uncertainty related to the dimensionless spin parameter, which are commonly required in the literature.