Abstract
In this paper, we use the equation of state based on a modification of 2+1 flavors Nambu-Jona- Lasinio (NJL) model to study the quark matter of hybrid stars. For comparison, we utilize five EOSs of the relativistic mean-field (RMF) model to describe the hadronic phase. With the 3- window crossover interpolation approach, we try to construct relatively soft hybrid EOSs but find the maximum masses of hybrid stars do not differ too much. The results are quite close to two solar mass, which is consistent with the mass constraint of PSR J0348+0432. Furthermore it is noteworthy that the heaviest stable stars have central densities higher than that of the deconfinement transition thus suggesting a pure quark core in the hybrid star.
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