Massive neutron stars with a hyperonic core: A case study with the IUFSU relativistic effective interaction

The recent discoveries of massive neutron stars, such as PSR J$0348+0432$ and PSR J$1614–2230$, have raised questions about the existence of exotic matter such as hyperons in the neutron star core. The validity of many established equations of states (EoSs) like GM1 and FSUGold are also questioned. We investigate the existence of hyperonic matter in the central regions of massive neutron stars by using relativistic mean field (RMF) theory with the recently proposed Indiana University Florida State University (IUFSU) model. The IUFSU model is extended by including hyperons to study the neutron star in $\beta$ equilibrium. The effect of different hyperonic potentials, namely $\Sigma$ and $\Xi$ potentials, on the EoS and hence the maximum mass of neutron stars has been studied. We have also considered the effect of stellar rotation since the observed massive stars are pulsars. It has been found that a maximum mass of $1.93M_{\odot }$, which is within the $3\sigma$ limit of the observed mass of PSR J$0348+0432$, can be obtained for rotating stars, with certain choices of the hyperonic potentials. The said star contains a fair amount of hyperons near the core.

Figure 1

(a) EoS obtained with varying $U_{\Sigma }^{\left(N\right)}$ at fixed $U_{\Xi }^{\left(N\right)}$. The upper branch shows the EoS for a system containing nucleons, leptons, and all the nonstrange mesons. The middle branch shows the EoS for a system containing the whole baryon octet, the leptons, and the $\sigma$, $\omega$, $\rho$, and $\varphi$ mesons. The lower branch shows the EoS for the particles contained in the middle branch except $\varphi$. (b) EoS obtained with varying $U_{\Xi }^{\left(N\right)}$ at fixed $U_{\Sigma }^{\left(N\right)}$. The compositions of the upper, middle and lower branches are same as those of panel (a), respectively.

Figure 2

Particle fractions for different $\Sigma$ potential depths: (a) for “$\sigma \omega \rho$” with $U_{\Sigma }^{\left(N\right)}=-30$ MeV, (b) for “$\sigma \omega \rho$” with $U_{\Sigma }^{\left(N\right)}=+30$ MeV, (c) for “$\sigma \omega \rho \varphi$” with $U_{\Sigma }^{\left(N\right)}=-30$ MeV, and (d) for “$\sigma \omega \rho \varphi$” with $U_{\Sigma }^{\left(N\right)}=+30$ MeV. $U_{\Xi }^{\left(N\right)}$ is fixed at $-18$ MeV in each case.

Figure 3

Particle fractions for different $\Xi$ potential depths: (a) for “$\sigma \omega \rho$” with $U_{\Xi }^{\left(N\right)}=-30$ MeV, (b) for “$\sigma \omega \rho$” with $U_{\Xi }^{\left(N\right)}=+30$ MeV, (c) for “$\sigma \omega \rho \varphi$” with $U_{\Xi }^{\left(N\right)}=-30$ MeV, (d) for “$\sigma \omega \rho \varphi$” with $U_{\Xi }^{\left(N\right)}=+30$ MeV. $U_{\Sigma }^{\left(N\right)}$ is fixed at +30 MeV in each case.

Figure 4

Mass-radius curves for static star fixing the (a) $\Xi$ potential depth at $U_{\Xi }^{\left(N\right)}=+40$ MeV and varying the $U_{\Sigma }^{\left(N\right)}$. (b) $\Sigma$ potential depth at $U_{\Sigma }^{\left(N\right)}=+40$ MeV and varying the $U_{\Xi }^{\left(N\right)}$. The uppermost curve in each case corresponds to the pure nuclear matter.

Figure 5

Mass-radius curves for rotating stars for two cases: (a) $U_{\Xi }^{\left(N\right)}=+40$ MeV and $-40\text{MeV}\le U_{\Sigma }^{\left(N\right)}\le +40$ MeV and (b) $U_{\Sigma }^{\left(N\right)}=+40$ MeV and $-40\text{MeV}\le U_{\Xi }^{\left(N\right)}\le +40$ MeV. The uppermost curve in each case corresponds to the pure nuclear matter.

Figure 6

Particle densities varying with radius along the equator. The potential depths for which particle densities are plotted are $U_{\Xi }^{\left(N\right)}=0$ and $U_{\Sigma }^{\left(N\right)}=+40$ MeV.