Unified EoS within Nambu–Jona-Lasinio description of hadronic matter from a Bayesian approach

# Introduction to the Unified Equations of State Dataset for Neutron Star Properties

This dataset comprises three unified equations of state (EOS) for neutron star properties, denoted as eNJL1, eNJL2, and eNJL3, developed based on a microscopic nuclear matter formalism with explicit chiral symmetry. This formalism is grounded in the Nambu Jona-Lasinio (NJL) model and has been specifically designed to accurately describe nuclear matter by introducing four-point and eight-point interactions. These interactions are crucial for reproducing nuclear matter properties at saturation density.

### Background and Methodology

To ensure the robustness and accuracy of the model parameters, a Bayesian inference approach was utilized. This method involved imposing constraints from experimental and {\it ab-initio} nuclear matter calculations, as well as observational data from neutron stars. Key properties such as the effective nucleon mass, radius, and maximum mass of neutron stars were meticulously matched against these constraints. The resulting model parameters provide a comprehensive and reliable description of nuclear matter and neutron star properties.

### Key Findings

- **Effective Nucleon Mass:** The model predicts an effective nucleon mass range between 0.75 and 0.8 times the nucleon mass.- **Neutron Star Radius:** At a 90% confidence level, the radius of a 1.4 $M_\odot$ neutron star varies between 11.48 km and 13.20 km.- **Maximum Mass and Radius:** The model predicts neutron stars with masses up to approximately 2.2 $M_\odot$, with the radius of a 2 $M_\odot$ star being above 10.5 km.- **Speed of Sound:** The speed of sound in the center of massive stars increases monotonically with density, reaching values between $\sqrt{0.7}c$ and $\sqrt{0.8}c$.

### High-Density Constraints and Observational Alignment

The high-density perturbative QCD (pQCD) results impose significant constraints on the EOS, invalidating those predicting larger maximum masses and radii. Interestingly, the EOS that satisfy pQCD constraints also align closely with recent mass-radius measurements, particularly those of PSR J0437-4715. This alignment provides an additional layer of validation against other relativistic mean field model results.

### Dataset Overview

This dataset includes three distinct EOS models (eNJL1, eNJL2, and eNJL3), each offering a unified approach for calculating neutron star properties. These models are detailed in the associated article, where the implications of the findings and the methodology are thoroughly discussed.

Researchers and astrophysicists can utilize this dataset to further explore and model the properties of neutron stars, contributing to a deeper understanding of these fascinating celestial objects. The provided EOS models are essential tools for simulations and theoretical studies aimed at deciphering the complex nature of neutron stars and nuclear matter under extreme conditions.