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The equations of state for neutron matter, strange and non-strange hadronic matter in the chiral SU(3) quark mean-field model are applied in the study of slowly rotating neutron stars and hadronic stars. It is shown that the rotation can increase the maximum mass of compact stars significantly, however the mass of the strange hadronic star is still not big enough to explain the observed extremely heavy pulsar, because of the weak equation of state of strange hadronic matter in this model. Inner structure of neutron star (From Prog. Part. Nucl. Phys. 54 (2005) 193) Slowly Rotating Neutron Stars and Hadronic StarsShaoyu Yin, Jiadong Zang, and Ru-Keng Su Euro. Phys. Jour. A 43 (2010) 295-301 Physics Department, Fudan University, 220 Handan Road, 200433, Shanghai, China neutron non-strange hadronic The EoS in chiral SU(3) quark mean field model (Phys. Rev. C 72 (2005) 045801) strange hadronic consider the relativistic rotation effect on the stellar mass and radius 3 Linear order, l=0 correction of the spherical harmonics 4 1 TOV Equation Metric 2 M-R relation of Strange hadronic star under rotation Conclusion: The range of the mass is significantly enlarged when the rotation is considered. However, the maximum mass of the strange hadronic star is still not large enough to explain the mass of PSR J1903+0327. Possible future work: 1. Consider the non-uniform rotation with larger core speed. 2. Modify the too soft EoS of the strange hadronic matter.