The Effect of a Self-bound Equation of State on the Structure of Rotating Compact Stars

TL;DR

The paper investigates how self-bound equations of state, notably strange quark stars, alter rotation-driven changes in gravitational mass and equatorial radius and how this affects universal relations. Using axisymmetric rotating-star models produced with the Rapidly Rotating Neutron Star code and several MIT bag-model plus linear self-bound EOSs, the authors show substantial deviations from existing universal relations as the surface-to-central energy-density ratio grows. They develop an inverse-mapping framework and introduce new empirical relations tailored to self-bound EOSs, significantly reducing mass and radius prediction errors (to about $\sim$6.7% in mass and $\sim$2.8% in radius for representative cases). The deviations are interpreted through the conservation of gravitational-potential differences in both GR and Newtonian limits, leading to a generalized radius-change expression and deeper insight into why self-bound stars obey near-universal trends under certain conditions. Practically, the improved relations enhance EOS inference for rapidly rotating compact objects, with relevance for NICER and gravitational-wave analyses as observational precision improves.

Abstract

This paper investigates how a self bound equation of state (EOS), which describes strange quark stars, affects the rotational properties of compact stars, focusing on deviations from universal relations governing gravitational mass and radius changes due to rotation. The analysis reveals significant deviations in stars with higher surface-to-center total energy-density ratios, $\frac{ε_s}{ε_c+c^2P_c}$, challenging the established universal relations. For Newtonian stars, hydrostatic equilibrium ensures that the difference between the gravitational potential at the center, $Φ_c$, and at the poles, $Φ_p$, remains constant within sequences of rotating neutron stars characterized by the same central and polar specific enthalpy ($Φ_c - Φ_p = -h_c +h_p$). Combined with the scaling $Φ\propto R_e^2$, where $R_e$ denotes the equatorial radius, this condition naturally leads to a quasi-universal behavior in the rotational change of radius within these sequences. Similarly, in general relativistic stars, the hydrostatic equilibrium maintains that $Φ^{GR}_{p} - Φ^{GR}_{c}$ remains unchanged within these sequences, where $Φ^{GR}$ is one of the metric potentials. Inspired by this theoretical framework, a toy model has been developed to capture the dependence of gravitational mass and radius deviations on the surface-to-central total energy density ratio. Subsequently, an improved set of empirical universal relations has been proposed, for accurately modeling rapidly rotating compact stars with self-bound EOSs.

Figures (1)

• Figure 1: Mass-radius plots for rotating strange quark stars. The star points in the mass-radius plots (a) and (b), represent strange quark stars with B = 60 $MeV/fm^3$ (QS60), with their corresponding spin frequencies-to-Kepler frequency ratio indicated by the color gradient. The dotted colored points illustrate the results of inverse mapping, as predicted by the universal relations. The difference in (a) and (b) is that for the inverse mapping in (a) the old universal relations has been used, while for (b) the updated version of the universal relations is adapted. Above and to the right of figures (a) and (b), the percent deviation of the equatorial radius and gravitational mass from the universal relations derived for normal EOSs is displayed. Figures (c) and (d) show the percent deviation of the change of the equatorial radius, while (e) and (f) show the percent deviation of the change of the gravitational mass, of the 15 strange quark star EOSs created in Section \ref{['strEOS1']}. Again, the plots on the left show the case where the old universal relations have been used, while the plots on the right illustrate the update that is introduced in this work. This visual representation allows for a clear comparison between the 15 self-bound stars and the predictions from normal EOS-based universal relations.