arXiv2024
Recent studies based on the relativistic mean field (RMF) model found certain nuclear empirical parameters, in particular the nucleon effective mass, to be strongly correlated with observable properties of Neutron Stars (NSs), such as the frequencies of $f-$mode oscillations. This shows the potential to constrain the values of effective mass from future observations of $f-$modes. One of our primary goals of this work is to investigate whether such correlations are physical or an artifact of the underlying nuclear model. To test this, we perform a comparative study of the correlations between NS astrophysical observables and nuclear physics parameters using two different equation of state models based on RMF theory and non-relativistic Meta-Modelling (MM) scheme. The nuclear meta-model does not assume any underlying nuclear model and therefore allows us to test the model dependence of the results. The calculations of the $f-$mode characteristics are performed within the relativistic Cowling approximation. We use state-of-the-art nuclear microscopic calculations at low density and multi-messenger astrophysical data at high-density within a Bayesian-inspired scheme to constrain the parameter space of the nuclear models. From the posterior distribution, we probe the underlying correlations among nuclear parameters and with NS observables. We find that the correlation between the symmetry energy and its slope is physical, while that of the nucleon effective mass with NS observables is model-dependent. The study shows that the effective mass governs the high density behaviour in RMF models, while in the MM it is controlled by the higher order saturation parameters, and hence probes the possibility of constraining them from future $f$-mode observations. The findings of this investigation are interesting both for astrophysics as well as nuclear physics communities.