Inertial modes in stratified rotating neutron stars: An evolutionary description

International audienceWith (nonbarotropic) equations of state valid even when the neutron, proton, and electron content of neutron star cores is not in beta equilibrium, we study inertial and composition gravity modes of relativistic rotating neutron stars. We solve the relativistic Euler equations in the time domain with a three dimensional numerical code based on spectral methods, in the slow rotation, relativistic Cowling and anelastic approximations. Principally, after a short description of the gravity modes due to smooth composition gradients, we focus our analysis on the question of how the inertial modes are affected by nonbarotropicity of the nuclear matter. In our study, the deviation with respect to barotropicity results from the frozen composition of nonsuperfluid matter composed of neutrons, protons, and electrons, when beta equilibrium is broken by millisecond oscillations. We show that already for moderately fast rotating stars the increasing coupling between polar and axial modes makes those two cases less different than for very slowly rotating stars. In addition, as we directly solve the Euler equations, without coupling only a few number of spherical harmonics, we always find, for the models that we use, a discrete spectrum for the l=m=2 inertial mode. Finally, we conclude that, for nonbarotropic stars, the frequency of this mode, which is our main focus, decreases in a non-negligible way, whereas the time dependence of the energy transfer between polar and axial modes is substantially different due to the existence of low-frequencies gravity modes