A new parametric equation of state and quark stars

TL;DR

This paper proposes a new parametric equation of state for quark stars based on a two-Gaussian potential, demonstrating stable crystalline structures and mass-radius relations consistent with observations, thus advancing understanding of cold quark matter.

Contribution

It introduces a novel parametric model for quark star matter using a two-Gaussian potential, linking microscopic interactions to macroscopic star properties.

Findings

Stable simple cubic crystal structure of quark clusters is possible.

Mass-radius relations similar to bag model predictions are achieved.

Maximum quark star mass ranges from 0.5 to 3 solar masses, consistent with observed pulsars.

Abstract

It is still a matter of debate to understand the equation of state of cold supra-nuclear matter in compact stars because of unknown on-perturbative strong interaction between quarks. Nevertheless, it is speculated from an astrophysical view point that quark clusters could form in cold quark matter due to strong coupling at realistic baryon densities. Although it is hard to calculate this conjectured matter from first principles, one can expect the inter-cluster interaction to share some general features to nucleon-nucleon interaction. We adopt a two-Gaussian component soft-core potential with these general features and show that quark clusters can form stable simple cubic crystal structure if we assume Gaussian form wave function. With this parameterizing, Tolman-Oppenheimer-Volkoff equation is solved with reasonable constrained parameter space to give mass-radius relation of crystalline solid quark star. With baryon densities truncated at 2 times nuclear density at surface and range of interaction fixed at 2fm we can reproduce similar mass-radius relation to that obtained with bag model equations of state. The maximum mass ranges from about 0.5 to 3 solar mass. Observed maximum pulsar mass (about 2 solar mass) is then used to constrain parameters of this simple interaction potential.