Vetting quark-star models with gravitational waves in the hierarchical Bayesian framework

TL;DR

This paper demonstrates how hierarchical Bayesian inference can be used to constrain the equation of state of quark stars using gravitational wave data, highlighting the potential and limitations of current models.

Contribution

It introduces a novel application of hierarchical Bayesian inference to jointly analyze multiple GW observations for quark star EOS constraints.

Findings

Constraints on $B_{eff}$ and $$ are significantly improved.

The 2-d EOS model shows biases in parameter estimation with more data.

The $m$-$$ relation remains consistent despite model simplifications.

Abstract

The recent discovery of gravitational waves (GWs) has opened a new avenue for investigating the equation of state (EOS) of dense matter in compact stars, which is an outstanding problem in astronomy and nuclear physics. In the future, next-generation (XG) GW detectors will be constructed, deemed to provide a large number of high-precision observations. We investigate the potential of constraining the EOS of quark stars (QSs) with high-precision measurements of mass $m$ and tidal deformability $\Lambda$ from the XG GW observatories. We adopt the widely-used bag model for QSs, consisting of four microscopic parameters: the effective bag constant $B_{\rm eff}$, the perturbative quantum chromodynamics correction parameter $a_4$, the strange quark mass $m_s$, and the pairing energy gap $\Delta$. With the help of hierarchical Bayesian inference, for the first time we are able to infer the EOS of QSs combining multiple GW observations. Using the top 25 loudest GW events in our simulation, we find that, the constraints on $B_{\rm eff}$ and $\Delta$ are tightened by several times, while $a_4$ and $m_s$ are still poorly constrained. We also study a simplified 2-dimensional (2-d) EOS model which was recently proposed in literature. The 2-d model is found to exhibit significant parameter-estimation biases as more GW events are analyzed, while the predicted $m$-$\Lambda$ relation remains consistent with the full model.