Finite temperature effects on g-modes of inviscid neutron stars

We study the effect of temperature on secular, compositional $g$-modes in the core of inviscid neutron stars. Using a chiral $SU(2)_f$ sigma model, we construct isentropic temperature profiles for hot and dense matter and find that the frequency of the global core $g$-mode's dependence on temperature is governed by the nuclear symmetry energy slope parameter $L$. As a result, the $g$-mode frequency of a warm neutron star can be either higher or lower than that of its cold counterpart, depending on $L$. Our results highlight the interplay of thermal effects and composition gradients, and demonstrate the potential of neutron star $g$-mode observations to constrain the density dependence of the symmetry energy.