Cold quark matter in a quasiparticle model: thermodynamic consistency and stellar properties

TL;DR

This paper develops a thermodynamically consistent quasiparticle model with a running coupling for $ud$ quark matter, and explores implications for the maximum mass of quark stars constrained by gravitational wave observations.

Contribution

It introduces a method to ensure thermodynamic consistency in quasiparticle models with a running coupling, and applies it to estimate quark star masses.

Findings

Maximum $ud$ quark star mass exceeds 2 solar masses.

Tidal deformability constraints limit maximum mass to about 2.08 solar masses.

Model confirms thermodynamic consistency with a running coupling.

Abstract

The strong coupling in the effective quark mass was usually taken as a constant in a quasiparticle model while it is, in fact, running with an energy scale. With a running coupling, however, the thermodynamic inconsistency problem appears in the conventional treatment. We show that the renormalization subtraction point should be taken as a function of the summation of the biquadratic chemical potentials if the quark's current masses vanish, in order to ensure full thermodynamic consistency. Taking the simplest form, we study the properties of up-down ($ud$) quark matter, and confirm that the revised quasiparticle model fulfills the quantitative criteria for thermodynamic consistency. Moreover, we find that the maximum mass of an $ud$ quark star can be larger than two times the solar mass, reaching up to $2.31M_{\odot}$, for reasonable model parameters. However, to further satisfy the upper limit of tidal deformability $\tilde{\Lambda}_{1.4}\leq 580$ observed in the event GW170817, the maximum mass of an $ud$ quark star can only be as large as $2.08M_{\odot}$, namely $M_{\text{max}}\lesssim2.08M_{\odot}$. In other words, our results indicate that the measured tidal deformability for event GW170817 places an upper bound on the maximum mass of $ud$ quark stars, but which does not rule out the possibility of the existence of quark stars composed of $ud$ quark matter, with a mass of about two times the solar mass.