# Equation-of-state Constraints and the QCD Phase Transition in the Era of Gravitational-Wave Astronomy

## TL;DR

This paper uses gravitational-wave data from GW170817 to set lower limits on neutron star radii, explores signatures of QCD phase transitions in neutron star mergers, and discusses implications for nuclear matter properties.

## Contribution

It provides the first robust lower limit on neutron star radii from GW data and identifies a potential gravitational-wave signature of a QCD phase transition during mergers.

## Key findings

- Neutron star radii are constrained to be larger than about 10.7 km.
- A strong first-order phase transition causes a significant shift in postmerger gravitational-wave frequency.
- Electromagnetic signals are not significantly affected by the phase transition, complicating observational identification.

## Abstract

We describe a multi-messenger interpretation of GW170817, which yields a robust lower limit on NS radii. This excludes NSs with radii smaller than about 10.7 km and thus rules out very soft nuclear matter. We stress the potential of this type of constraints when future detections become available. A very similar argumentation may yield an upper bound on the maximum mass of nonrotating NSs. We also discuss simulations of NS mergers, which undergo a first-order phase transition to quark matter. We point out a different dynamical behavior. Considering the gravitational-wave signal, we identify an unambiguous signature of the QCD phase transition in NS mergers. The occurrence of quark matter through a strong first-order phase transition during merging leads to a characteristic shift of the dominant postmerger frequency. The frequency shift is indicative for a phase transition if it is compared to the postmerger frequency which is expected for purely hadronic EoS models. A very strong deviation of several 100 Hz is observed for hybrid EoSs in an otherwise tight relation between the tidal deformability and the postmerger frequency. We address the potential impact of a first-order phase transition on the electromagnetic counterpart of NS mergers. Our simulations suggest that there would be no significant qualitative differences between a system undergoing a phase transition to quark matter and purely hadronic mergers. The quantitative differences are within the spread which is found between different hadronic EoS models. This implies on the one hand that GW170817 is compatible with a possible transition to quark matter. On the other hand these considerations show that it may not be easy to identify quantitative differences between purely hadronic mergers and events in which quark matter occurs considering solely their electromagnetic counterpart or their nucleosynthesis products. (abridged)