A quark model with running coupling and running strange quark mass, which is thermodynamically self-consistent at both high and lower densities, is presented and applied to study properties of strange quark matter and structure of compact stars. An additional term to the thermodynamic potential density is determined by meeting the fundamental differential equation of thermodynamics. It plays an important role in comparatively lower density and ignorable at extremely high density, acting as a chemical-potential dependent bag constant. In this thermodynamically enhanced perturbative QCD model, strange quark matter still has the possibility of being absolutely stable, while the pure quark star has a sharp surface with a maximum mass as large as about 2 times the solar mass and a maximum radius of about 11 kilometers.

The possible existence of stable up-down quark matter ($ud$QM) was recently proposed, and it was shown that the properties of $ud$QM stars are consistent with various pulsar observations. In this work we investigate the stability of $ud$QM nuggets and found at certain size those objects are more stable than others if a large symmetry energy and a small surface tension were adopted. In such cases, a crust made of $ud$QM nuggets exists in quark stars. A new family of white dwarfs comprised entirely of $ud$QM nuggets and electrons were also obtained, where the maximum mass approaches to the Chandrasekhar limit.

The interface effects of quark matter play important roles in the properties of compact stars and small nuggets, such as strangelets and nonstrange quark matter ($ud\mathrm{QM}$) nuggets. By introducing a density derivative term to the Lagrangian density and adopting Thomas-Fermi approximation, we find it is possible to reproduce the results obtained by solving Dirac equations. Adopting certain parameter sets, the energy per baryon of $ud\mathrm{QM}$ nuggets decreases with baryon number $A$ and become more stable than nuclei at $A\gtrsim 300$. The effects of quark matter symmetry energy are examined, where $ud\mathrm{QM}$ nuggets at $A\approx 1000$ can be more stable than others if large symmetry energy is adopted. In such cases, larger $ud\mathrm{QM}$ nuggets will decay via fission and the surface of a $ud\mathrm{QM}$ star will fragment into a crust made of $ud\mathrm{QM}$ nuggets and electrons, which resembles the cases of a strange star’s crust. The corresponding microscopic structures are then investigated adopting spherical and cylindrical approximations for the Wigner-Seitz cells, where the droplet phase is found to be the most stable configuration with $ud\mathrm{QM}$ stars’ crusts and $ud\mathrm{QM}$ dwarfs made of $ud\mathrm{QM}$ nuggets ($A\approx 1000$) and electrons. For the cases considered here, the crust thickness of $ud\mathrm{QM}$ stars is typically $\sim 200\mathrm{m}$, which reaches a few kilometers if we neglect the interface effects and adopt Gibbs construction. The masses and radii of $ud\mathrm{QM}$ dwarfs are smaller than typical white dwarfs, which would increase if the interface effects are neglected.

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 2 times the solar mass, reaching up to $2.31M_{\odot }$, for reasonable model parameters. However, to further satisfy the upper limit of tidal deformability ${\tilde{\mathrm{\Lambda }}}_{1.4}\le 580$ observed in the event GW170817, the maximum mass of an $ud$ quark star can only be as large as $2.08M_{\odot }$, namely $M_{\max }\lesssim 2.08M_{\odot }$. 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 does not rule out the possibility of the existence of quark stars composed of $ud$ quark matter, with a mass of about 2 times the solar mass.