# Quark-Nuclear Hybrid EoS with Excluded Volume Effects

## TL;DR

This paper develops a hybrid equation of state for quark-nuclear matter incorporating excluded volume effects, leading to predictions of hybrid stars with mass-radius relations satisfying observational constraints.

## Contribution

It introduces a two-phase model with excluded volume effects in both phases, providing new insights into the stiffening of matter and hybrid star properties.

## Key findings

- Predicts hybrid stars with a third family branch.
- Achieves mass-radius relations satisfying the 2 solar mass constraint.
- Shows stiffening of matter due to excluded volume effects.

## Abstract

A two-phase description of the quark-nuclear matter hybrid equation of state that takes into account the effect of excluded volume in both the hadronic and the quark matter phases is introduced. The nuclear phase manifests a reduction of the available volume as density increases, leading to a stiffening of the matter. The quark matter phase displays a reduction of the effective string tension in the confining density functional from available volume contributions. The nuclear equation of state is based upon the relativistic density functional model DD2 with excluded volume. The quark matter is based upon a mean-field modification to the free fermi gas and will be discussed in greater detail. The interactions are decomposed into mean scalar and vector components. The scalar interaction is motivated by a string potential between quarks, whereas the vector interaction potential is motivated by higher order interactions of quarks leading to an increased stiffening at high densities. As an application, we consider matter under compact star constraints of electric neutrality and $\beta$-equilibrium. We obtain mass-radius relations for hybrid stars that form a third family, disconnected from the purely hadronic star branch, and fulfill the $2M_\odot$ constraint.