Narrow Results

The property difference between the neutron star PSR J0348$+$0432 and its proto neutron star is studied in the framework of the relativistic mean field theory considering neutrino trapping. We see that the central baryon number density of the proto neutron star PSR J0348+0432 is in the range ${\rho }_{c,\mathrm{\text{PNS}}}=0.539\text{–}0.698$fm${}^{-3}$, which is smaller than that of the neutron star PSR J0348$+$0432 ${\rho }_{c,\mathrm{\text{NS}}}=0.634\text{–}0.859$fm${}^{-3}$. Inside the neutron star PSR J0348$+$0432, only the neutrons, protons, $\mathrm{\Lambda }$ and ${\mathrm{\Xi }}^{-}$ produce, whereas the hyperons ${\mathrm{\Sigma }}^{-},{\mathrm{\Sigma }}^0,{\mathrm{\Sigma }}^{+}$ and ${\mathrm{\Xi }}^0$ all do not appear. But in the proto neutron star PSR J0348$+$0432, hyperons ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, ${\mathrm{\Sigma }}^{+}$ and ${\mathrm{\Xi }}^0$ all will produce, though their relative particle number density is still very small, no more than 2%. This shows that higher temperature will be advantageous to the hyperon production.

The properties of proto neutron star (PNS) PSR J0740+6620 are studied with the relative mean field theory. In our calculations, we find that five nucleon coupling parameters (DD-MEI, NL1, NL2, TW99 and GM1) can give the mass of the PNS PSR J0740+6620. The radius of PNS PSR J0740+6620 calculated by GM1 is the smallest, $R=14.63$–$13.44$km, and that calculated by TW99 is the largest, $R=17.46$–$17.07$km. The radius calculated by other nucleon coupling parameters is between the two. We find that properties of PNS PSR J0740+6620 calculated by different nucleon coupling parameters are different. The central baryon density ${\rho }_c$, the central field strength ${\sigma }_{0c}$, ${\omega }_{0c}$, ${\sigma }_{0c}^{\ast }$ and ${\varphi }_{0c}$ of mesons $\sigma$, $\omega$, ${\sigma }^{\ast }$ and $\varphi$, the central energy density ${𝜀}_c$, and the central pressure $p_c$ calculated by GM1 are all the largest among the five sets of nucleon coupling parameters. The calculations with DD-MEI, TW99 and GM1 show that eight baryons (n, p, $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, ${\mathrm{\Sigma }}^{+}$, ${\mathrm{\Xi }}^{-}$ and ${\mathrm{\Xi }}^0$) appear inside PNS PSR J0740+6620 whereas those with NL1 and NL2 show that hyperon ${\mathrm{\Sigma }}^{+}$ does not appear. The relative particle density of baryons inside PNS PSR J0740+6620 is also very different as the PNS is calculated with different nucleon coupling constants.