Yan Xu, Xiulin Huang, yibo Wang, Qi Yuan, Wen-Bo Ding, Ning An, Yufu Shen, Zi Yu
Abstract The temperature dependence of neutron star structure significantly alters the equation of state, thereby affecting observable properties such as the moment of inertia and gravitational redshift. Utilizing the relativistic mean-field (RMF) theory with hyperonic degrees of freedom under SU(3) flavor and SU(6) spin-flavor symmetries, we investigate the thermal effects on the structural properties of protoneutron stars (PNSs) and cold neutron stars (CNSs). Focusing on PSR J1012+5307, we analyze the drastic structural transformations occurring during the transition from a PNS to a CNS. For a 1.94 $M_{\odot}$ hyperonic star under SU(3) flavor symmetry, decreasing the temperature from $T = 30$ MeV to 0 MeV induces a radius contraction of approximately 50$\% $, accompanied by a drop in the moment of inertia by nearly 26$\%$ and a significant increase in gravitational redshift by approximately 154$\%$. Furthermore, we examine the variations in the moment of inertia and gravitational redshift arising from mass uncertainties of PSR J1012+5307. Taking SU(3) flavor symmetry at $T=20$ MeV as an example, increasing the mass across the range 1.72 $M_{\odot}$$-$$1.94 M_{\odot}$ results in a radius contraction of 2.749 km, an $\sim$8\% increase in the moment of inertia, and a significant $\sim$40\% increase in the gravitational redshift. We find that in the cold regime and at a fixed mass, the radius, moment of inertia, and gravitational redshift of hyperonic matter under SU(3) flavor symmetry differ only marginally from those of purely nucleonic matter, rendering it difficult to observationally confirm the presence of hyperons in the core of PSR~J1012+5307. Moreover, future observations capable of precisely constraining pulsar masses—ideally through long-term monitoring from birth—hold the potential to determine more conclusively whether hyperons or other exotic matter reside in individual pulsars.