# Hot quark matter and (proto-) neutron stars

## TL;DR

This paper explores the QCD phase diagram and the composition of hot and cold neutron star matter, revealing the conditions for phase transitions and the presence of hyperons and $\Delta$-isobars in stellar models.

## Contribution

It introduces a non-local Polyakov-Nambu-Jona-Lasinio model to analyze the QCD phase diagram and investigates the baryonic composition of proto-neutron stars, including hyperons and $\Delta$-isobars.

## Key findings

- Identification of a spinodal region in the QCD phase diagram.
- Hot stellar models contain hyperons and $\Delta$-isobars but no deconfined quarks.
- Deconfined quarks appear only in cold neutron stars.

## Abstract

In part one of this paper, we use a non-local extension of the 3-flavor Polyakov-Nambu-Jona-Lasinio model, which takes into account flavor-mixing, momentum dependent quark masses, and vector interactions among quarks, to investigate the possible existence of a spinodal region (determined by the vanishing of the speed of sound) in the QCD phase diagram and determine the temperature and chemical potential of the critical end point. In part two of the paper, we investigate the quark-hadron composition of baryonic matter at zero as well as non-zero temperature. This is of great topical interest for the analysis and interpretation of neutron star merger events such as GW170817. With this in mind, we determine the composition of proto-neutron star matter for entropies and lepton fractions that are typical of such matter. These compositions are used to delineate the evolution of proto-neutron stars to neutron stars in the baryon-mass versus gravitational-mass diagram. The hot stellar models turn out to contain significant fractions of hyperons and $\Delta$-isobars but no deconfined quarks. The latter, are found to exist only in cold neutron stars.