Quadrupole moments of rotating neutron stars

TL;DR

This work computes the quadrupole moments of rotating neutron stars to quantify rotation-induced deformations that affect the exterior gravitational field. Using the rns code and Ryan's GR multipole framework, the authors evaluate $Q$ for four EOS across masses $1.0$–$1.8\,M_\odot$ and angular momenta from $J=0$ to $J_{\max}$, revealing that $|Q|$ increases with EOS stiffness. A robust quadratic relation $q \simeq -a(M,\text{EOS})\, \chi^2$ with $\chi = cJ/(G M^2)$ describes the data, leading to $Q \simeq -\frac{a(M,\text{EOS})}{c^2} \frac{J^2}{M}$, with the coefficient $a$ decreasing as mass grows. The results hold even near the Kepler limit, highlighting a simple, EOS- and mass-dependent model for neutron-star quadrupoles with relevance to gravitational-wave modeling of binary systems.

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.

Figures (5)

• Figure 1: Plots of $q$ as a function of $\chi$ for four equations of state, for neutron stars of mass $M=1.0\ M_\odot$. The data of Table 2 is shown with circles, and the solid curves represent the fits of Eq. (\ref{['27']}).
• Figure 2: Same as Fig. 1 but with $M=1.2\ M_\odot$. The circles represent the data of Table 3.
• Figure 3: Same as Fig. 1 but with $M=1.4\ M_\odot$. The circles represent the data of Table 4.
• Figure 4: Same as Fig. 1 but with $M=1.6\ M_\odot$. The circles represent the data of Table 5.
• Figure 5: Same as Fig. 1 but with $M=1.8\ M_\odot$. The circles represent the data of Table 6.