The Potential Well-Depth ${U_{Sigma}^{(N)}}$ Constraints on the Surface Gravitational Red-shift of a Proto Neutron Star

The influence of the potential well depth U_S^(N)U_{Sigma}^{(N)} of Σ in nuclear matter on the surface gravitational red-shift of a proto neutron star is examined within the framework of the relativistic mean field theory for the baryon octet system. It is found that as U_S^(N)U_{Sigma}^{(N)} increases from −35 MeV to +35 MeV, the surface gravitational red-shift increases and the influence of the negative U_S^(N)U_{Sigma}^{(N)} on the surface gravitational red-shift is larger than that of the positive ones. Furthermore, the M _max/R and the surface gravitational red-shift corresponding to the maximum mass all increase as the U_S^(N)U_{Sigma}^{(N)} increases, M _max and R being the maximum mass of the proto neutron star and the corresponding radius respectively.