[Paper Review] Bayesian analysis of multimessenger M-R data with interpolated hybrid EoS

Alexander Ayriyan, D. Blaschke+4 more|arXiv (Cornell University)|Feb 26, 2021

Pulsars and Gravitational Waves Research88 references52 citations

TL;DR

This paper presents a Bayesian analysis of multimessenger neutron star data using a novel two-zone parabolic interpolation between a soft hadronic EoS (APR) and a stiff color-superconducting quark matter EoS based on a nonlocal NJL model with two free parameters (ηD, ηV). The key result is that the data strongly favor a color-superconducting quark phase with ηD ≈ 0.75, and the most probable EoS cannot support a maximum mass above 2.5 M⊙, implying GW190814 was likely a binary black hole merger rather than a neutron star–black hole system.

ABSTRACT

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a set of stiff quark matter EoS at high densities within a finite region of chemical potentials $\mu_H < \mu < \mu_Q$. Fixing the hadronic EoS as the APR one and choosing the color-superconducting, nonlocal NJL model with two free parameters for the quark phase, we perform Bayesian analyses with this two-parameter family of hybrid EoS. Using three different sets of observational constraints that include the mass of PSR J0740+6620, the tidal deformability for GW170817, and the mass-radius relation for PSR J0030+0451 from NICER as obligatory (set 1), while set 2 uses the possible upper limit on the maximum mass from GW170817 as an additional constraint and set 3 instead of the possibility that the lighter object in the asymmetric binary merger GW190814 is a neutron star. We confirm that in any case, the quark matter phase has to be color superconducting with the dimensionless diquark coupling approximately fulfilling the Fierz relation $\eta_D=0.75$ and the most probable solutions exhibiting a proportionality between $\eta_D$ and $\eta_V$, the coupling of the repulsive vector interaction that is required for a sufficiently large maximum mass. We used the Bayesian analysis to investigate with the method of fictitious measurements the consequences of anticipating different radii for the massive $2~M_\odot$ PSR J0740+6220 for the most likely equation of state. With the actual outcome of the NICER radius measurement on PSR J0740+6220 we could conclude that for the most likely hybrid star EoS would not support a maximum mass as large as $2.5~M_\odot$ so that the event GW190814 was a binary black hole merger.

Motivation & Objective

• To develop a flexible, physically motivated family of hybrid neutron star equations of state (EoS) using two-zone parabolic interpolation between hadronic and quark matter phases.
• To perform a Bayesian analysis of multimessenger constraints (mass, radius, tidal deformability) to infer posterior distributions over EoS parameters.
• To test the robustness of EoS constraints under different observational assumptions, including the nature of the compact object in GW190814.
• To assess the predictive power of the method using fictitious NICER radius measurements for PSR J0740+6620.
• To determine whether the observed maximum mass of 2.14 M⊙ in PSR J0740+6620 is compatible with hybrid EoS models supporting higher masses.

Proposed method

• Construct a two-parameter family of hybrid EoS by interpolating between the soft APR EoS at low densities and a nonlocal NJL model for color-superconducting quark matter at high densities.
• Use a parabolic interpolation in chemical potential space between µH = 991 MeV (n ≈ 1.5n₀) and µQ, ensuring smooth transition and avoiding unphysical reconfinement.
• Apply Bayesian inference with three distinct observational constraint sets: (1) PSR J0740+6620 mass, GW170817 tidal deformability, and NICER J0030+0451 radius; (2) adds upper limit on Mmax from GW170817; (3) assumes GW190814's lighter component is a neutron star.
• Use the method of fictitious measurements to simulate future NICER radius measurements for PSR J0740+6620 and assess their impact on EoS inference.
• Compute posterior probabilities for EoS models and compare results across constraint sets using relative posterior normalization.
• Analyze the resulting M–R sequences, EoS pressure–energy density relations, and tidal deformability correlations (Λ1–Λ2) to extract physical constraints.

Experimental results

Research questions

• RQ1 Can a two-zone parabolic interpolation between hadronic and quark matter EoS produce physically viable hybrid stars without unphysical reconfinement?
• RQ2 What are the posterior constraints on the diquark coupling (ηD) and vector interaction strength (ηV) in a color-superconducting quark matter phase?
• RQ3 Does the inclusion of the PSR J0740+6620 mass and radius as constraints favor EoS models with higher maximum masses?
• RQ4 Is the observed mass of 2.14 M⊙ in PSR J0740+6620 compatible with hybrid EoS models that also satisfy GW170817 and NICER constraints?
• RQ5 What is the likelihood that GW190814 was a neutron star–black hole merger, given the inferred EoS constraints?

Key findings

• The Bayesian analysis favors a color-superconducting quark matter phase with the diquark coupling ηD ≈ 0.75, consistent with the Fierz relation.
• The most probable EoS solutions exhibit a strong correlation between ηD and ηV, where the repulsive vector interaction (ηV) is essential for achieving a sufficiently large maximum neutron star mass.
• The inferred EoS family cannot support a maximum mass exceeding 2.5 M⊙, which rules out the scenario that GW190814 involved a neutron star with mass ≈2.6 M⊙.
• The actual NICER radius measurement for PSR J0740+6620 (R ≈ 11.4 km) implies that the most likely hybrid EoS would not support a 2.5 M⊙ star, reinforcing the conclusion that GW190814 was likely a binary black hole merger.
• The method of fictitious measurements successfully predicts that future NICER radius measurements for PSR J0740+6620 would significantly constrain the EoS, especially in the high-density regime.
• The relative posterior probability of the present EoS model family is more than five times higher than that of a previous model (Ref. [11]) when using the same set of constraints (set 1), indicating improved data compatibility.