# What neutron stars tell about the hadron-quark phase transition: a Bayesian study

## TL;DR

This study uses Bayesian analysis to explore the possibility of quark matter inside neutron stars, finding that a pure quark core is unlikely above certain mass thresholds and highlighting the significance of the speed of sound peak.

## Contribution

It introduces a Bayesian framework combining multiple models to constrain the hadron-quark phase transition parameters using recent neutron star observations.

## Key findings

- Pure quark cores are only possible if neutron star masses are below ~2.35 M_sun.
- A peak in the speed of sound exceeding 1/3 is strongly favored by data.
- The phase transition parameters are sensitive to astrophysical constraints, but the speed of sound peak position remains stable.

## Abstract

The existence of quark matter inside the heaviest neutron stars has been the topic of numerous recent studies, many of them suggesting that a phase transition to strongly interacting conformal matter inside neutron stars is feasible. Here we examine this hybrid star scenario using a soft and a stiff hadronic model, a constituent quark model with three quark flavours, and applying a smooth crossover transition between the two. Within a Bayesian framework, we study the effect of up-to-date constraints from neutron star observations on the equation-of-state parameters and various neutron star observables. Our results show that a pure quark core is only possible if the maximum mass of neutron stars is below $\sim2.35~M_\odot$. However, we also find, consistently with other studies, that a peak in the speed of sound, exceeding $1/3$, is highly favoured by astrophysical measurements, which might indicate the percolation of hadrons at $\sim3-4n_0$. Even though our prediction for the phase transition parameters varies depending on the specific astrophysical constraints utilized, the position of the speed of sound peak only changes slightly, while the existence of pure quark matter below $\sim4 n_0$, using our parameterization, is disfavoured. On the other hand, the preferred range for the EoS shows signs of conformality above $\sim4n_0$. Additionally, we present the difference in the upper bounds of radius estimates using the full probability density data and sharp cut-offs, and stress the necessity of using the former.