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Lennard-Jones quark matter and massive quark stars

Quark clustering could occur in cold quark matter because of the strong coupling between quarks at realistic baryon densities of compact stars. Although one may still not be able to calculate this conjectured matter from first principles, the inter-cluster interaction might be analogized to the interaction between inert molecules. Cold quark matter would then crystallize in a solid state if the inter-cluster potential is deep enough to trap the clusters in the wells. We apply the Lennard-Jones potential to describe the inter-cluster potential, and derive the equations of state, which are stiffer than that derived in conventional models (e.g., MIT bag model). If quark stars are composed of Lennard-Jones matter, they could have high maximum masses ($>2M_{\odot}$) as well as very low masses ($<10^{-3}M_{\odot}$). These features could be tested by observations.