Deconfinement Phase Transition in Compact Stars : Maxwell vs. Gibbs Construction of the Mixed Phase

TL;DR

This paper compares Maxwell and Gibbs constructions for the deconfinement phase transition in compact stars, revealing significant differences in star properties and matter composition, with implications for electric field formation.

Contribution

It provides a detailed comparison of Maxwell and Gibbs constructions in modeling the deconfinement transition within compact stars, highlighting their impact on star properties and matter distribution.

Findings

Maxwell construction causes a sharp density discontinuity.

Gibbs construction results in a smooth transition.

Sharp electron chemical potential jump may induce electric fields.

Abstract

We study different realisations of the first order deconfinement phase transition inside a compact star by comparing the Gibbs and Maxwell construction for the mixed phase. The hadronic sector is described within the relativistic mean field model including hyperons. The quark sector is described by the MIT Bag model. We find that these two realisations lead to very different star properties, in particular, the composition of the stellar matter. We also find that for the Maxwell construction there is a sharp discontinuity in the baryon density and the electron chemical potential. We argue that a sharp jump in the elctron chemical potential should lead to the redistribution of electrons and formation of strong electric fields around the discontinuity surface.