Interface effects of quark matter: Light-quark nuggets and compact stars

The interface effects of quark matter play important roles in the properties of compact stars and small nuggets such as strangelets and $ud$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 $ud$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 $ud$QM nuggets at $A\approx 1000$ can be more stable than others if large symmetry energy is adopted. In such cases, larger $ud$QM nuggets will decay via fission and the surface of an $ud$QM star will fragment into a crust made of $ud$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 $ud$QM stars' crusts and $ud$QM dwarfs made of $ud$QM nuggets ($A\approx 1000$) and electrons. For the cases considered here, the crust thickness of $ud$QM stars is typically $\sim$200 m, which reaches a few kilometers if we neglect the interface effects and adopt Gibbs construction. The masses and radii of $ud$QM dwarfs are smaller than typical white dwarfs, which would increase if the interface effects are neglected.