Learning the relations between neutron star and nuclear matter properties with symbolic regression

TL;DR

This work addresses the challenge of linking neutron-star observables to underlying nuclear-matter properties by applying symbolic regression (via PySR) and PCA to RMF-based EOS datasets constrained by Bayesian inference. By analyzing two datasets—NL (nucleons only) and NL-hyp (including hyperons)—the authors reveal a robust, interpretable relationship between the 1.4 solar-mass NS tidal deformability and the $2\rho_0$ beta-equilibrium pressure, with iso-vector nuclear-matter properties dominating the NS response. Hyperons modify correlations at higher densities, but including hyperon fractions (notably $X^\Xi$) can recover predictive power for proton fractions and preserve key links between NS properties and symmetry-energy parameters. Overall, the study provides physics-informed, interpretable relationships that constrain the EOS at supra-saturation densities and illustrate how ML tools can bridge nuclear physics and astrophysical observables.

Abstract

The equation of state (EOS) of dense matter in neutron stars (NSs) remains uncertain, particularly at supra-nuclear densities where complex nuclear interactions and the potential presence of exotic matter, like hyperons, come into play. The complex relationships existing between nuclear matter and neutron star properties are investigated. The focus is on their nonlinearities and interdependencies. In our analysis, we apply a machine learning algorithm known as symbolic regression, paired with principal component analysis, to datasets generated from Bayesian inference over relativistic mean-field models. A systematic Principal Component Analysis has allowed to break down the percentage contribution of each element or feature in the relationships obtained. This study examines two main models (datasets): the NL model, which includes nucleonic degrees of freedom; and the NL-hyp model, which includes hyperons in addition to nucleons. Our analysis confirms a robust correlation between the tidal deformability of a 1.4 \(M_\odot\) neutron star and $β$-equilibrium pressure at twice the nuclear saturation density. This correlation remains once hyperons are included. The contribution of the different nuclear matter properties at saturation to the radius and tidal deformability was calculated. It was shown that the isovector properties have the largest impact, with a contribution of about 90\%. We also studied the relationship between the proton fraction at different densities and various symmetry energy parameters defined at saturation density. For the hyperon data set, we took into account the effects of the negatively charged hyperon $Ξ$ in order to recover the relationships. Our study reveals the individual impact of various symmetry energy parameters on proton fractions at different densities.

Figures (4)

• Figure 1: The pie chart illustrates the percentage contribution of the saturation properties to the proton fraction ($X^p$) for NL (upper) and NL-hyp (bottom), as indicated in Table \ref{['tab1']}.
• Figure 2: The values of the percentage contributions of NMPs to the radius and tidal deformability of NS with masses range $1.2-1.8M_\odot$ (refer to Table \ref{['tab2']}).
• Figure 3: The Pearson's correlation coefficients among few selected quantities in NL dataset.
• Figure 4: Same as Fig.\ref{['fig3']} but for NL-hyp dataset.