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

TL;DR

This work investigates whether correlations between nuclear empirical parameters and neutron-star observables are intrinsic or artifacts of the chosen nuclear model. By directly comparing two EoS frameworks—Relativistic Mean Field (RMF) and a model-agnostic Meta-Model (MM)—the authors examine NS mass–radius, tidal deformability, and $f$-mode frequencies calculated in the relativistic Cowling approximation, under a Bayesian-inspired constraint scheme that includes low-density $\chi$EFT and high-density multi-messenger observations. A key finding is that the symmetry-energy parameters $J_{sym}$ and $L_{sym}$ exhibit a physical, model-independent correlation, while the correlation between the Dirac effective mass $m^*_D/m$ and NS observables is strongly model-dependent, appearing in RMF but not in MM where high-density behavior is governed by higher-order parameters ($K_{sym}$, $Q_{sat}$, $Q_{sym}$, $Z_{sym}$). The MM results indicate that high-density NS physics can be constrained by these higher-order parameters, whereas RMF results emphasize the role of $m^*_D/m$, highlighting the importance of model choice in NS asteroseismology. Overall, the study clarifies which nuclear parameters can be robustly constrained from future $f$-mode observations and how complementary data at different densities help disentangle underlying physics.

Abstract

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.

Figures (15)

• Figure 1: The variation of energy per baryon ($E/A$) with baryon number density ($n_B$) for pure neutron matter has been plotted. The bands display theoretical $\chi$EFT uncertainty at next-to-next-to-next-to-leading order (N$^3$LO). These bands are taken from drischler2016_PRCKeller_Hebeler_2023prl. See text for further details.
• Figure 2: Mass-radius $(M$-$R)$ relations due to variation in higher-order parameters ($K_{sym}$, $Q_{sat}$, $Z_{sat}$, $Q_{sym}$, $Z_{sym}$) and the Landau effective mass ($m^*_L/m$) within Meta-model framework. The individual parameters are varied around their central values (when others are fixed at the central values) within their uncertainties from Table \ref{['tab:MM_params_uncertainties']}.
• Figure 3: Dimensionless tidal deformability ($\Lambda$) as a function of Neutron Star mass for variation in $K_{sym}$, $Q_{sat}$, $Z_{sat}$, $Q_{sym}$, $Z_{sym}$, and $m^*_L/m$ within Meta-model framework. The individual parameters are varied around their central values (when others are fixed at the central values) within their uncertainties from Table \ref{['tab:MM_params_uncertainties']}.
• Figure 4: $f-$mode frequency as a function of Neutron Star mass for variation in $K_{sym}$, $Q_{sat}$, $Z_{sat}$, $Q_{sym}$, $Z_{sym}$, and $m^*_L/m$ within Meta-model framework. The individual parameters are varied around their central values (when others are fixed at the central values) within their uncertainties from Table \ref{['tab:MM_params_uncertainties']}.
• Figure 5: Mass-radius relations for posterior ANM EoSs within RMF framework after applying $\chi$EFT (Drischler et al. 2016 drischler2016_PRC) and Astro filters. The $68\%$ and $95\%$ contours of the NICER mass-radius measurements are shown by dark and light regions, respectively Rutherford_2024Salmi_2024Vinciguerra_2024Choudhury_2024. (See text for more details)