Bayesian Quantification of Observability and Equation of State of Twin Stars

TL;DR

This work investigates the existence and observability of neutron star twin stars—pairs of stars with identical mass but different radii—within a nine-parameter EOS meta-model that spans hadronic and quark matter regimes. Using a Bayesian framework informed by GW170817 radius data, the authors map EOS parameters to mass-radius topologies and quantify twin-star observability through ΔM and ΔR, finding that 12–18% of EOSs can produce twins under varied branch-length criteria. They reveal category-dependent PDFs for high-density QM parameters, notably a two-peak structure in c_qm^2 for the Both category, suggesting density-dependent stiffness of quark matter. Effects of recent NICER measurements show that high-mass radius constraints tend to shrink the twin-star parameter space, while certain NICER data can moderately enhance twin-star occurrences; overall, twin stars, if observed, would significantly constrain the underlying EOS and illuminate the QM phase diagram at neutron-star densities.

Abstract

The possibility of discovering twin stars, two neutron stars (NSs) with the same mass but different radii, is usually studied in forward modelings by using a restricted number of NS matter equation of state (EOS) encapsulating a first-order phase transition from hadronic to quark matter (QM). Informing our likelihood function with the NS radius data from GW170817 and using a meta-model with 9-parameters capable of mimicking most NS EOSs available in the literature, we conduct a Bayesian quantification of the observability and underlying EOSs of twin stars. Of the accepted EOSs, between 12-18\% yield twin stars, depending on the restrictions we place on the second branch. The possibility of twin stars remains robust even under recent observational constraints. We show that many of these twin star scenarios are observable with currently available levels of accuracy in measuring NS radii. We also present the marginalized posterior probability density functions (PDFs) of every EOS parameter for each of four mass-radius correlation topologies. We find that the inferred EOS depends sensitively on not only whether twin stars are present, but also the category of twin stars, indicating that the observation of twin stars would provide a strong constraint on the underlying EOS. In particular, for two coexisting hybrid stars having QM cores at different densities, the PDF for QM speed of sound squared $c_{\rm qm}^2$ has two peaks, one below and another above the conformal limit $c_{\rm qm}^2=1/3$ predicted by perturbative QCD.

Figures (10)

• Figure 1: Modified slightly from Fig. 2 in Ref. Alford:2013aca, these diagrams show an exaggerated MR curve for each category. The change from black to red marks the appearance of QM in the core. Dashed lines represent unstable configurations. Shown in the right panel are $\Delta M$, which is the difference between the maximum mass on the first branch and the minimum mass of the second branch, and $\Delta R$, which is the maximum radius difference between twins. The $\Delta M$ and $\Delta R$ together are used to measure the observability of twin stars ZhangLi_twin.
• Figure 2: Probability densities for how observable twin stars are. Top, the mass range over which twin stars are observable with the probability in log-scale. Bottom, the largest radius difference possible between twin stars.
• Figure 3: PDFs of QM parameters.
• Figure 4: PDFs of high-density HM EOS parameters
• Figure 5: Probability distribution of M$_{\rm{TOV}}$ (top), the maximum mass reached on the first branch (middle), and the maximum mass reached on the second branch (bottom) of all accepted EOSs in their respective categories.