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Quark matter symmetry energy and quark stars

We extend the confined-density-dependent-mass (CDDM) model to include isospin dependence of the equivalent quark mass. Within the confined-isospin-density-dependent-mass (CIDDM) model, we study the quark matter symmetry energy, the stability of strange quark matter, and the properties of quark stars. We find that including isospin dependence of the equivalent quark mass can significantly influence the quark matter symmetry energy as well as the properties of strange quark matter and quark stars. While the recently discovered large mass pulsars PSR J1614-2230 and PSR J0348+0432 with masses around $2M_{\odot}$ cannot be quark stars within the CDDM model, they can be well described by quark stars in the CIDDM model. In particular, our results indicate that the two-flavor $u$-$d$ quark matter symmetry energy should be at least about twice that of a free quark gas or normal quark matter within conventional Nambu-Jona-Lasinio model in order to describe the PSR J1614-2230 and PSR J0348+0432 as quark stars.