Neutron stars (NSs) are ideal astrophysical laboratories for testing theories of dense matter and provide connections among astrophysics, nuclear and particle physics. The recent discoveries of the binary millisecond pulsars PSR J0952-0607, PSR J0740+6620, PSR J0348+0432 and PSR J1614-2230 suggest that the maximum mass Mmax lie within 2.

35±0. 17M⊙, 2.

08 ± 0. 07 M⊙, 2.

01 ± 0. 04 M⊙ and 1.

97 ± 0. 04 M⊙ respectively, where M⊙ is the solar mass.

The largest mass measurements are powerfully influencing the behavior of nuclear symmetry energy near the nuclear saturation density and the high-density equation of state (EoS) because of the existence of the maximum mass. The properties of pure hadronic and hybrid compact stars using a suitable realistic nuclear equation of state for β-equilibrated neutron star matter are discussed here.

We have employed the pure hadronic EoS and the EoS combined with quark for the ultra-dense inner core to determine the mass of NS. The significant reduction of maximum mass has been found with the inclusion of quark core.

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