DOI: 10.5281/zenodo.17534438
title: A Bayesian Inference of Hybrid Stars with Large Quark Cores

description: We provide data from the equations of state (EoS), the TOV results, and the parameters of the NJL, MFTQCD, RMF, NJL-GW, and r-NJL sets from arXiv: 2511.02653.

We also provide codes that plot EoS (plot_eos.py) and TOV (plot_mr_lambda.py) graphs for a chosen set and model indices.

 

Abstract:

Neutron stars (NSs) are interesting objects capable of reaching densities unattainable on Earth. The properties of matter under these conditions remain a mystery. Exotic matter, including quark matter, may be present in the NS core. In this work, we explore the possible compositions of NS cores, in particular, the possible existence of large quark cores. We use the Relativistic Mean Field (RMF) model with nonlinear terms for the hadron phase and the Nambu–Jona-Lasinio (NJL) model and Mean Field Theory of Quantum Chromodynamics (MFTQCD) for the quark phase. Through Bayesian inference, we obtain different sets of equations: four sets with hybrid equations (three using the NJL model and the other using the MFTQCD model), and one set with only the hadron phase. We impose constraints regarding the properties of nuclear matter, X-ray observational data from NICER, perturbative QCD (pQCD) calculations, and causality on all sets. One set of hybrid NJL equations of state was also constrained by adding the GW170817 detection. All sets can describe observational data and theoretical restrictions. The MFTQCD allows for a phase transition to quark matter at lower densities compared to the NJL models. The MFTQCD model indicates that NSs with 1.4 M$_\odot$ have quark matter in their inner core. However, NJL models suggest that it is more probable that 1.4 M$_\odot$ NSs do not contain quark matter. Both the MFTQCD and NJL models agree that there is quark matter in 2 M$_\odot$ NSs. It is discussed that hybrid stars with a stiff quark equation of state could explain a larger radius of more massive stars, such as two solar mass stars, with respect to the canonical NS.

 

File organization:

Each set has a directory with the respective files:

par_[X].dat:



contains the parameters of the models

it has the following columns:



NJL, NJL-GW and r-NJL sets:



model: model index;

quark parameters: xio ($\xi_\omega$), xir ($\xi_\rho$), xioo ($\xi_{\omega\omega}$), xios ($\xi_{\omega\sigma}$), xior ($\xi_{\omega\rho}$), B (MeV/fm$^3$);

hadron parameters: g_sigma ($g_\sigma$), g_omega ($g_\omega$), g_rho ($g_\rho$), BB ($b \times 10^3$), CC ($c \times 10^3$), xi ($\xi$), lam ($\Lambda_\omega$);



MFTQCD set:



model: model index;

quark parameters: xiQ ($\xi_Q$, MeV$^{-1}$), B (MeV/fm$^3$);

hadron parameters: g_sigma ($g_\sigma$), g_omega ($g_\omega$), g_rho ($g_\rho$), BB ($b \times 10^3$), CC ($c \times 10^3$), xi ($\xi$), lam ($\Lambda_\omega$);



MFTQCD set:



model: model index;

hadron parameters: g_sigma ($g_\sigma$), g_omega ($g_\omega$), g_rho ($g_\rho$), BB ($b \times 10^3$), CC ($c \times 10^3$), xi ($\xi$), lam ($\Lambda_\omega$).






eos_[X].dat:



contains the equations of state of the X model

it has the following columns:



model: model index;

muB: baryonic chemical potential (MeV);

rhoB: baryonic density (fm$^{-3}$);

P: pressure (MeV/fm$^3$);

eps: energy density (MeV/fm$^3$);

cs2: speed of sound;

gamma: polytropic index;

Delta: trace anomaly;

dc: measure of conformability.




tov_[X].dat:



contains the results of the TOV equations

it has the following columns:



model: model index;

P0: central pressure (MeV/fm$^3$);

R: radius (km);

M: mass (m_sun);

Lambda: tidal deformability.