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Bayesian constraints on quark stars from multi-messenger observations

Wen-Jie Xie, Cheng-Jun Xia, Chen Zhang, Renxin Xu

TL;DR

This work performs a comprehensive Bayesian analysis of quark-star EOSs within an interacting MIT bag model that includes color-superconducting phases. By comparing two prior selections and assessing the impact of the GW190814 secondary mass, the study shows that current observations strongly constrain the bulk stiffness via the effective bag constant $B$, while the detailed phase structure (2SC vs CFL) remains largely indistinguishable in macroscopic observables. The results indicate that self-bound quark stars naturally accommodate the low-mass object HESS J1731-347, whereas extreme-mass inferences are highly prior-dependent, underscoring the need for careful prior-sensitivity analyses. A two-parameter reduction to $(B,g)$ preserves information about the EOS and tightens constraints on $B$, with sound speeds $v_s^2$ consistently exceeding the conformal limit $1/3$ across densities, highlighting robust high-density behavior and guiding future multimessenger tests of quark-star viability.

Abstract

We perform a systematic Bayesian analysis of quark star equations of state under current multimessenger constraints, investigating the impact of prior assumptions and extreme-mass observations. Quark matter is modeled within an interacting MIT bag framework that consistently accommodates color-superconducting phases (2SC, 2SC+s, and CFL) and perturbative QCD corrections. We find that quark star models exhibit a distinct advantage in naturally accommodating the ultra-low mass object HESS J1731-347, a configuration that is challenging for standard neutron star models. In the high-mass regime, the interpretation of the secondary component of GW190814 is shown to be strongly prior-dependent: only broad priors allow for the substantial stiffness required to support such a massive object ($\sim$2.6 M$_\odot$), while more restrictive priors favor a softer equation of state consistent with standard pulsar populations. Microscopically, we demonstrate that current data tightly constrain the effective bag constant and the overall stiffness, but cannot distinguish between different color-superconducting phases. Furthermore, we validate a reduction of the model to two effective parameters without loss of information. Our results indicate that if quark stars exist, their sound speeds consistently exceeds the conformal limit ($c_s^2>1/3$) at stellar densities.

Bayesian constraints on quark stars from multi-messenger observations

TL;DR

This work performs a comprehensive Bayesian analysis of quark-star EOSs within an interacting MIT bag model that includes color-superconducting phases. By comparing two prior selections and assessing the impact of the GW190814 secondary mass, the study shows that current observations strongly constrain the bulk stiffness via the effective bag constant , while the detailed phase structure (2SC vs CFL) remains largely indistinguishable in macroscopic observables. The results indicate that self-bound quark stars naturally accommodate the low-mass object HESS J1731-347, whereas extreme-mass inferences are highly prior-dependent, underscoring the need for careful prior-sensitivity analyses. A two-parameter reduction to preserves information about the EOS and tightens constraints on , with sound speeds consistently exceeding the conformal limit across densities, highlighting robust high-density behavior and guiding future multimessenger tests of quark-star viability.

Abstract

We perform a systematic Bayesian analysis of quark star equations of state under current multimessenger constraints, investigating the impact of prior assumptions and extreme-mass observations. Quark matter is modeled within an interacting MIT bag framework that consistently accommodates color-superconducting phases (2SC, 2SC+s, and CFL) and perturbative QCD corrections. We find that quark star models exhibit a distinct advantage in naturally accommodating the ultra-low mass object HESS J1731-347, a configuration that is challenging for standard neutron star models. In the high-mass regime, the interpretation of the secondary component of GW190814 is shown to be strongly prior-dependent: only broad priors allow for the substantial stiffness required to support such a massive object (2.6 M), while more restrictive priors favor a softer equation of state consistent with standard pulsar populations. Microscopically, we demonstrate that current data tightly constrain the effective bag constant and the overall stiffness, but cannot distinguish between different color-superconducting phases. Furthermore, we validate a reduction of the model to two effective parameters without loss of information. Our results indicate that if quark stars exist, their sound speeds consistently exceeds the conformal limit () at stellar densities.

Paper Structure

This paper contains 13 sections, 16 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. EQUATIONS OF STATE AND BAYESIAN FRAMEWORK
  3. Quark matter equation of state
  4. Effective parameter reduction and physical interpretation
  5. Stellar structure and observable quantities
  6. Bayesian inference framework
  7. RESULTS AND DISCUSSION
  8. Global mass–radius properties of quark stars
  9. Macroscopic observables from the four-parameter model
  10. Posterior constraints on microscopic quark matter parameters
  11. Reduced quark star models: three- and two-parameter descriptions
  12. Equation of state and sound speed
  13. Conclusion and Outlook

Figures (12)

  • Figure 1: (Color online) Mass-radius constraints at $90\%$ credibility for quark stars in the CFL, 2SC+s, and 2SC phases. The calculations for quark stars are based on a four-parameter model with the "Prior-1" parameter distributions. Observational constraints from NICER (PSRs J0030+0451 Miller2019_ApJ887-L24Riley2019_ApJ887-L21, J0740+6620 Miller2021_ApJ918-L28Riley2021_ApJ918-L27, J0437-4715Choudhury2024_ApJ971-L20) and HESS J1731-347 Doroshenko2022_NA6-1444 are shown for comparison. The left and right panels correspond to cases with and without the inclusion of the secondary component of GW190814 as a constraint, respectively.
  • Figure 2: (Color online) As in Fig. \ref{['fig:mr-pr1']}, but showing the results based on the four-parameter model with the "Prior-2" parameter distributions.
  • Figure 3: (Color online) Posterior probability distribution functions of the radius, tidal deformability corresponding to the quark stars with 1.4 and 2.0 solar masses, maximum mass and the corresponding radius, central squared speed of sound, central energy density and central pressure inferred from the Bayesian analysis of the data listed in Table \ref{['tab-data']} for the CFL, 2SC and 2SC+s phases.
  • Figure 4: (Color online) Posterior probability distribution functions of the radius, tidal deformability corresponding to the quark stars with 1.4 and 2.0 solar masses, maximum mass and the corresponding radius, central squared speed of sound, central energy density and central pressure inferred from the Bayesian analysis of the data listed in Table \ref{['tab-data']} for the CFL, 2SC and 2SC+s phases.
  • Figure 5: (Color online) Posterior probability distribution functions of the five parameters for the QM properties and their correlations at 68% (light shadow) and 90% (dark shadow) confidence levels inferred from the Bayesian analysis of the data listed in Table \ref{['tab-data']}. In the calculations, the Prior-1 set is used. The values showed in the corner are the 90% confidence intervals for the five parameters.
  • ...and 7 more figures