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Phase Structure of Compact Star in Modified Quark-Meson Coupling Model

The K$^-$ condensation and quark deconfinement phase transitions are investigated in the modified quark-meson coupling model. It is shown that K$^-$ condensation is suppressed because of the quark deconfinement when $B^{1/4}<$202.2MeV, where $B$ is the bag constant for unpaired quark matter. With the equation of state (EOS) solved self-consistently, we discuss the properties of compact stars. We find that the EOS of pure hadron matter with condensed K$^-$ phase should be ruled out by the redshift for star EXO0748-676, while EOS containing unpaired quark matter phase with $B^{1/4}$ being about 180MeV could be consistent with this observation and the best measured mass of star PSR 1913+16. We then probe into the change of the phase structures in possible compact stars with deconfinment phase as the central densities increase. But if the recent inferred massive star among Terzan 5 with M$>$1.68M$_{\odot}$ is confirmed, all the present EOSes with condensed phase and deconfined phase would be ruled out and therefore these exotic phases are unlikely to appear within neutron stars.