# Hybrid equation of state with pasta phases and third family of compact stars

## TL;DR

This paper examines how pasta phases influence the quark-hadron phase transition in neutron star matter, comparing numerical solutions with interpolating models, and explores the impact on hybrid star structure and the existence of a third family of compact stars.

## Contribution

It provides a detailed analysis of pasta phases' effects on phase transitions and introduces a mapping between model parameters and physical surface tension, extending to neutron star structure.

## Key findings

- Pasta phases significantly affect the quark-hadron phase transition.
- A fit formula relates the model parameter to surface tension.
- The third family of compact stars can be robust against pasta phase effects.

## Abstract

The effect of pasta phases on the quark-hadron phase transition is investigated for a set of relativistic mean-field equations of state for both hadron and quark matter. The results of the full numerical solution with pasta phases are compared with those of an interpolating construction used in previous works, for which we demonstrate an adequate description of the numerical results. A one-to-one mapping of the free parameter of the construction to the physical surface tension of the quark-hadron interface is obtained for which a fit formula is given. For each pair of quark and hadron matter models the critical value of the surface tension is determined, above which the phase transition becomes close to the Maxwell construction. This result agrees well with earlier theoretical estimates. The study is extended to neutron star matter in beta equilibrium with electrons and muons and is applied to investigate the effect of pasta phases on the structure of hybrid compact stars and the robustness of a possible third family solution.