Interface effects of quark matter: Light-quark nuggets and compact stars
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Abstract
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 $A\ensuremath{\gtrsim}300$. The effects of quark matter symmetry energy are examined, where $ud\mathrm{QM}$ nuggets at $A\ensuremath{\approx}1000$ 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 ($A\ensuremath{\approx}1000$) and electrons. For the cases considered here, the crust thickness of $ud\mathrm{QM}$ stars is typically $\ensuremath{\sim}200\text{ }\text{ }\mathrm{m}$, 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.