Equation-of-State Independent Relations in Rapidly Rotating Hybrid Stars

TL;DR

This paper investigates equation-of-state–independent (quasi-universal) relations for compact stars, spanning both slowly and rapidly rotating configurations, across a wide set of hadronic EoSs with heavy baryons and 100 hybrid EoSs with hadron–quark transitions. Using TOV, Hartle–Thorne, tidal perturbations, and KEH/RNS methods, it derives and fits relations among $C$, $k_2$, $ar{ lambda}$, $ar{I}$, and $ar{Q}$, demonstrating robust universality for hadronic cores and quantifying deviations when quark matter is present. The results show that $C$–$ar{ lambda}$ remains approximately EoS-insensitive with modest errors, while I–Love–Q relations degrade to about $ ext{O}(20 ext{%})$ when exotic cores are included; rapid rotation further increases scatter, though quasi-universal trends persist along fixed spin sequences. These findings provide practical tools to infer neutron-star radii and interior composition from observables, consistent with NICER and GW observations, and highlight both the utility and limits of universal relations in the presence of exotic dense matter.

Abstract

We study 22 hadronic and 100 hybrid equations of state (EoSs) that allow for heavy baryons and deconfined quark matter at high densities, aiming to establish quasi-universal relations for both slowly and rapidly rotating neutron stars. All EoSs are consistent with current observational constraints, including NICER and GW170817. Our results confirm that the I-Love-Q and I-C-Q relations remain approximately EoS-insensitive across this broad EoS set, with deviations typically within 10\% for hadronic stars and up to 20\% for those with complex core compositions. These relations are extended to include low-mass neutron stars such as HESS J1731-347, and to stars with general core compositions--nucleonic, hyperonic (full baryon octet), and quark matter. The analysis underscores both the robustness and the limitations of universal relations when applied to compact stars with exotic degrees of freedom and rapid rotation.

Figures (13)

• Figure 1: Hadronic EoSs for cold NS matter incorporating heavy baryon degrees of freedom. Subfigure (a) shows the pressure–energy density relations for various EoS models, while subfigure (b) presents the corresponding speed of sound squared, $c_s^2$, profiles. The colour coding is consistent across both subfigures.
• Figure 2: Hybrid EoSs, along with the hadronic EoSs, are shown in subfigure (a). Solid curves represent the hadronic EoSs, while dashed curves correspond to hybrid EoSs constructed via the Maxwell phase transition. Single-dot dashed curves indicate hybrid EoSs obtained from CompOSE, and double-dot dashed curves represent those generated using the replacement interpolation method (RIM). The associated speed of sound squared, $c_s^2$, for the considered EoSs is presented in subfigure (b). The colour scheme is the same across both subfigures.
• Figure 3: Mass-radius relations of CSs are shown in subfigures (a) and (b) for the static and Keplerian limits, respectively, using the full set of EoSs. NICER measurements for PSR J0030+0451 Miller_2019_dFNjMRiley_2019_oQUYh and PSR J0740+6620 Miller_2021_pAcGMRiley_2021_kbhlr (95% credible intervals) are overlaid. Subfigure (a) also includes the NS radius constraints inferred from GW170817 Abbott_2018_EX9Nk, NS mass-radius constraints for central compact object in HESS J1731--347 Doroshenko_2022_xyimd (68.3% and 95.4% credibility intervals), and the mass range estimated for the secondary component of GW190814 Abbott_2020_jIBsD is indicated. Identical colour codes are used in both subfigures.
• Figure 4: Variation of the dimensionless tidal Love number $k_2$ with compactness $C$ for the enitre EoS dataset.
• Figure 5: $C$–$\overline{\Lambda}$ relations obtained using (a) hadronic EoSs and (b) both hadronic and hybrid EoSs. The top panels display the data and fit; the bottom panels show corresponding fractional deviations.