Probing the nonstrange quark star equation of state with compact stars and gravitational waves

TL;DR

This work addresses thermodynamic inconsistencies in conventional perturbative QCD when applied to dense quark matter by introducing a self-consistent correction term $\Omega'$, yielding a total potential $\Omega = \Omega_{\mathrm{pt}} + \Omega'$. The authors constrain the equation of state for up-down ($ud$) quark matter by combining tidal deformability from GW170817 with mass-radius observations of massive pulsars, and they map the feasible parameter space in $(C, B_0^{1/4})$. They find that, under the constraint $\epsilon_{ud} \ge 930\,\text{MeV}$, the maximum quark-star mass is about $2.17\,M_\odot$, which reduces to $\sim 2.07$–$2.08\,M_\odot$ when GW170817 tidal data are included. Consequently, the compact object inferred in GW190814 ($2.59^{+0.08}_{-0.09}\,M_\odot$) is unlikely to be an $ud$ quark star within this revised pQCD framework, and the work highlights the potential of multi-messenger constraints to shape quark-matter models.

Abstract

A recent study shows that incorporating a new term into the thermodynamic potential density, as required by the thermodynamic consistency criterion, can effectively resolve the thermodynamic inconsistency problems of the conventional perturbative QCD model. This additional term plays a crucial role in resolving inconsistencies at relatively low densities and becomes negligible at extremely high densities. Within this revised perturbative QCD model, we find that if we require only that the energy per baryon of up-down ($ud$) quark matter exceeds 930 MeV so as not to contradict the standard nuclear physics, the maximum mass of an $ud$ quark star allowed by the revised perturbative QCD model can reach up to 2.17 $M_{\odot}$. From this perspective, the observed 2.14 $M_{\odot}$ pulsar PSR J0740+6620 may be an $ud$ quark star. However, if we further impose the constraint that the tidal deformability of a 1.4 $M_{\odot}$ $ud$ quark star must be consistent with the GW170817 event, the maximum mass allowed by the revised perturbative QCD model would decrease to no more than 2.08 $M_{\odot}$. Consequently, our results suggest that the compact object with a mass of 2.50-2.67 $M_{\odot}$, as observed in the GW190814 event, cannot be an $ud$ quark star, according to the revised perturbative QCD model.

Figures (6)

• Figure 1: Stability window for $ud$ quark matter in the $C-B_0^{1/4}$ plane. The bottom-right black shaded area is forbidden, where the energy per baryon of $ud$ quark matter is less than 930 MeV. Meanwhile, the orange shaded region between the blue dashed and blue dash-dotted curves with star symbols corresponds to the $ud$ quark matter stable region with an equation of state that can support an $ud$ quark star with the tidal deformability of a $1.4~M_{\odot}$ quark star in the range $70\leq \tilde{\Lambda}_{1.4}\leq 580$. The selected typical model parameters are indicated with black solid dots.
• Figure 2: Density behavior of the energy per baryon for different $C$ and $B_0$ values. The minimum energy and zero pressure are marked with inverted triangles and open circles, respectively.
• Figure 3: Equation of state of $ud$ quark matter for the same parameter sets as Fig. \ref{['fig:NbEnergy']}.
• Figure 4: The polytropic index as a function of the baryon density at zero temperature for the same parameter sets as Fig. \ref{['fig:NbEnergy']}.
• Figure 5: Mass-radius relations of quark stars for the same parameter sets as Fig. \ref{['fig:NbEnergy']}. The maximum masses of the $ud$ quark stars are indicated by black solid circles.