# Treating quarks within neutron stars

## TL;DR

This paper investigates the presence of deconfined quark cores in neutron stars using various phase transition models, finding that quarks appear at certain masses and can be consistent with observational constraints, but distinguishing hybrid stars remains challenging.

## Contribution

It systematically explores different quark-hadron transition scenarios in neutron stars and their compatibility with recent observational data, highlighting the conditions for quark core formation.

## Key findings

- Quarks appear in neutron stars with masses around 1.0-1.6 solar masses.
- Supported quark matter requires a squared speed of sound greater than 0.4.
- Certain equations of state are consistent with GW170817 tidal deformability bounds.

## Abstract

Neutron star interiors provide the opportunity to probe properties of cold dense matter in the QCD phase diagram. Utilizing models of dense matter in accord with nuclear systematics at nuclear densities, we investigate the compatibility of deconfined quark cores with current observational constraints on the maximum mass and tidal deformability of neutron stars. We explore various methods of implementing the hadron-to-quark phase transition, specifically, first-order transitions with sharp (Maxwell construction) and soft (Gibbs construction) interfaces, and smooth crossover transitions. We find that within the models we apply, hadronic matter has to be stiff for a first-order phase transition and soft for a crossover transition. In both scenarios and for the equations of state we employed, quarks appear at the center of pre-merger neutron stars in the mass range $\approx 1.0-1.6\,{\rm M}_{\odot}$, with a squared speed of sound $c^2_{\rm QM}\gtrsim 0.4$ characteristic of strong repulsive interactions required to support the recently discovered neutron star masses $\geq 2\,{\rm M}_{\odot}$. We also identify equations of state and phase transition scenarios that are consistent with the bounds placed on tidal deformations of neutron stars in the recent binary merger event GW170817. We emphasize that distinguishing hybrid stars with quark cores from normal hadronic stars is very difficult from the knowledge of masses and radii alone, unless drastic sharp transitions induce distinctive disconnected hybrid branches in the mass-radius relation.