Quadrupole moments of rotating neutron stars

TL;DR

This paper models rotating neutron stars with various equations of state, analyzing how their quadrupole moments depend on mass, angular momentum, and the equation of state, providing simple quadratic fits for Q as a function of J.

Contribution

It introduces detailed numerical models of rotating neutron stars for multiple equations of state and derives a simple quadratic relation for the quadrupole moment based on angular momentum.

Findings

|Q| increases with the stiffness of the equation of state for fixed M and J.

Q can be approximated by Q ≈ -a J^2 / (M c^2) with a parameter of order unity.

The dependence of Q on J is well described by a quadratic fit.

Abstract

Numerical models of rotating neutron stars are constructed for four equations of state using the computer code RNS written by Stergioulas. For five selected values of the star's gravitational mass (in the interval between 1.0 and 1.8 solar masses) and for each equation of state, the star's angular momentum is varied from J=0 to the Keplerian limit J=J_{max}. For each neutron-star configuration we compute Q, the quadrupole moment of the mass distribution. We show that for given values of M and J, |Q| increases with the stiffness of the equation of state. For fixed mass and equation of state, the dependence on J is well reproduced with a simple quadratic fit, Q \simeq - aJ^2/M c^2, where c is the speed of light, and a is a parameter of order unity depending on the mass and the equation of state.