# Massive Neutron Stars with a Color Superconducting Quark Matter Core

## TL;DR

This paper develops an equation of state for neutron star matter using the NJL model, demonstrating that neutron stars with color superconducting quark cores can exceed 2 solar masses, aligning with recent observations.

## Contribution

It shows that the same NJL model parameters can describe both nuclear and quark matter phases, predicting massive neutron stars with quark cores.

## Key findings

- Maximum neutron star mass exceeds 2.01 solar masses.
- Equation of state aligns with gravitational wave data.
- Color superconducting quark matter can be stable at high densities.

## Abstract

We construct the equation of state for high density neutron star matter at zero temperature using the two-flavor Nambu--Jona-Lasinio (NJL) model as an effective theory of QCD. We build nuclear matter, quark matter, and the mixed phases from the same NJL Lagrangian, which has been used to model free and in-medium hadrons as well as nuclear systems. A focus here is to determine if the same coupling constants in the scalar diquark and vector meson channels, which give a good description of nucleon structure and nuclear matter, can also be used for the color superconducting high density quark matter phase. We find that this is possible for the scalar diquark (pairing) interaction, but the vector meson interaction has to be reduced so that superconducting quark matter becomes the stable phase at high densities. We compare our equation of state with recent phenomenological parametrizations based on generic stability conditions for neutron stars. We find that the maximum mass of a neutron star, with a color superconducting quark matter core, exceeds $2.01 \pm 0.04\,M_\odot$ which is the value of the recently observed massive neutron star PSR J0348+0432. The mass-radius relation is also consistent with gravitational wave observations (GW170817).