Frozen and β-equilibrated f and p modes of cold neutron stars: Nuclear metamodel predictions

Context. When the chemical re-equilibration timescale is sufficiently long, the normal and quasi-normal mode frequencies of neutron stars should be calculated in the idealised limit that the internal composition of each fluid element is fixed over the oscillation period. However, many studies rely on a barotropic equation of state, implicitly overlooking potential out-of-β-equilibrium effects.Aims. We investigate potential biases that may arise from the assumption of purely barotropic models in studies of oscillation modes. To address this, we calculated the non-radial fundamental (f) and first pressure (p_{1) modes for a wide range of neutron star structures, each characterised by different nucleonic equations of state. This approach also yields posterior distributions for the oscillation frequencies, which could be detected by next-generation gravitational wave interferometers.Methods. A wide range of nuclear equations of state are generated with the metamodel technique, a phenomenological framework that incorporates constraints from astrophysical observations, experimental nuclear physics, and chiral effective field theory. The metamodel also provides the internal composition of β-equilibrated npeμ matter, allowing us to calculate oscillation modes beyond those supported by a purely barotropic fluid.Results. By exploiting the observed validity of quasi-universal relations, we developed a simple technique to estimate the general relativity corrections in relation to the commonly used Cowling approximation and provide a posterior predictive distribution of expected f- and p1-mode frequencies.}