Medium Effects in MIT Bag Model for quark matter: Self consistent thermodynamical treatment

TL;DR

This paper addresses thermodynamic inconsistencies in the density-dependent MIT Bag model for strange quark matter by proposing a chemical potential dependent Bag pressure, enabling self-consistent calculations of quark star properties.

Contribution

It introduces a new formulation of the Bag pressure dependent on chemical potential to ensure thermodynamic consistency in the grand canonical ensemble.

Findings

The proposed model satisfies the Euler relation and minimizes energy per baryon at zero pressure.

Mass-radius relations of strange stars are computed using the new formalism.

The approach allows for consistent modeling of quark star structures.

Abstract

The study of strange quark matter within the framework of the density-dependent MIT Bag model using the Grand Canonical ensemble is thermodynamically inconsistent. In this work, it is shown that if the medium effects are incorporated through a density-dependent Bag pressure in the Grand Canonical ensemble, then the Euler relation is violated. If Euler relation is used then the minimum of energy per baryon does not occur at zero pressure. In order to overcome this inconsistency, we propose the medium effect of the strange quark matter in the form of chemical potential dependent Bag pressure in the grand Canonical ensemble. The density dependent Bag pressure which has been used in Grand Canonical ensemble so far can however be used in Canonical ensemble without violating the laws of thermodynamics. These prescriptions will obey the Euler relation as well as the minimum energy per baryon will coincide with the zero of pressure and hence can be considered to be self consistent. These equations of state in the Grand Canonical ensemble can be further used to construct the Mass-Radius and other structural properties of the strange quark stars as well as hybrid stars. In our present work we have calculated the mass radius diagram of strange stars only using this formalism.