Investigating the role of nuclear parameters in Neutron Star oscillations: a model comparison

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.

💡 Research Summary

The paper investigates whether the strong correlations previously reported between the nucleon effective mass (m*/m) and observable neutron‑star (NS) properties—particularly the frequencies of the fundamental fluid (f‑mode) oscillations—are genuine physical relationships or artifacts of the specific nuclear model employed. To address this, the authors conduct a comparative analysis using two fundamentally different equations of state (EOS): a relativistic mean‑field (RMF) model, which is a phenomenological relativistic density functional, and a non‑relativistic meta‑modelling (MM) approach, which expands the energy per particle in terms of empirical nuclear parameters without assuming any underlying microscopic interaction.

Both models are constrained within a Bayesian‑inspired framework. At low densities (up to roughly 1.4 n_sat) the authors incorporate state‑of‑the‑art chiral effective field theory (χEFT) calculations and experimental nuclear data (binding energies, neutron‑skin thicknesses, dipole polarizabilities, giant monopole resonances). At higher densities they impose multi‑messenger astrophysical constraints: the existence of ≳2 M⊙ pulsars, NICER mass‑radius measurements, and the tidal deformability Λ inferred from the GW170817 binary‑neutron‑star merger. These constraints generate posterior distributions for the model parameters.

The f‑mode frequencies are computed in the relativistic Cowling approximation, which neglects metric perturbations but retains the relativistic structure of the background star. Although this approximation underestimates the true frequencies by about 20 % compared with full general‑relativistic calculations, it preserves the qualitative dependence of the frequencies on the underlying EOS parameters, making it suitable for a systematic correlation study.

The analysis reveals two key findings. First, the correlation between the symmetry energy at saturation (J_sym) and its slope (L_sym) is robust: it appears in both the RMF and MM posterior samples with high statistical significance. This indicates that the J–L correlation is a genuine physical feature of dense matter, reflecting how the isovector part of the nuclear interaction controls the pressure of neutron‑rich matter and thus the NS radius and tidal deformability.

Second, the previously reported strong correlation between the nucleon effective mass and NS observables is model‑dependent. In the RMF framework, the Dirac effective mass m*_D/m directly influences the scalar mean field, which in turn governs the stiffness of the EOS at supra‑saturation densities. Consequently, variations in m*_D/m produce sizable changes in the f‑mode frequency, leading to a pronounced correlation in the RMF posterior. In contrast, within the MM formalism the effective mass parameter does not dominate the high‑density pressure; instead, higher‑order saturation parameters such as the isoscalar skewness Q_sat, the isovector curvature K_sym, and higher‑order terms control the EOS stiffness. The MM posterior therefore shows little or no correlation between m*/m and the f‑mode frequency, while still exhibiting sensitivity to those higher‑order coefficients.

These results demonstrate that the effective‑mass–f‑mode correlation is an artifact of the specific functional form of the RMF model rather than a universal property of dense nuclear matter. The study thus cautions against using f‑mode observations to directly constrain the effective mass without accounting for model dependence. Instead, future detections of f‑mode gravitational waves could be employed to constrain the higher‑order saturation parameters that dominate the EOS in model‑agnostic approaches like meta‑modelling.

The paper also discusses the implications for nuclear physics and astrophysics. For nuclear theorists, the work underscores the importance of exploring a broad class of EOS parametrizations when interpreting astrophysical data, to avoid spurious parameter correlations. For astrophysicists, it highlights that upcoming missions (e.g., NICER, eXTP) and gravitational‑wave observatories (e.g., Advanced LIGO/Virgo, third‑generation detectors) could, through precise f‑mode frequency measurements, provide novel constraints on the density dependence of the symmetry energy and on higher‑order bulk nuclear parameters, thereby sharpening our understanding of the dense‑matter equation of state.

In summary, the authors provide a rigorous, model‑independent assessment of the link between nuclear empirical parameters and neutron‑star oscillation properties, confirming the physical nature of the symmetry‑energy correlation while revealing the model‑specific nature of the effective‑mass correlation. This work paves the way for more reliable extraction of nuclear‑matter information from future multimessenger observations of neutron stars.