An Asymptotically Causal Metamodel for Neutron Star Equations of State

Abstract

Nuclear metamodels - phenomenological parametrizations of the energy of nuclear matter - are convenient tools to explore the space of realistic neutron star configurations constrained by astrophysical and nuclear data. While much recent work has focused on composition-agnostic barotropic models, the metamodel approach is designed to describe the composition dependence of the relevant thermodynamic potential. We revise a previously proposed non-relativistic metamodel by introducing a more controlled high-density behaviour, improving both its causal properties and its accuracy in reproducing the pressure and the beta-equilibrium composition of microscopically motivated equations of state. Since causality is automatically enforced at high density, the fraction of discarded models due to superluminal sound speeds is substantially reduced, facilitating metamodel-based explorations of equilibrium neutron star configurations. We further assess our framework by performing a Bayesian inference of neutron star properties beyond standard observables such as masses and radii, exploiting the metamodel's ability to probe composition-dependent quantities including the dUrca threshold and the Ledoux criterion for g-mode stability.

Figures (10)

• Figure 1: Comparison of fitted and original energy per baryon. Top panels show the original and fitted $e_X(n,\delta)$ for SNM ($\delta=0$, left) and PNM ($\delta=1$, right); bottom panels show the differences between the original and fitted models in MeV.
• Figure 2: Comparison of physical quantities across models: (a) energy density, (b) pressure, (c) proton fraction, (d) equilibrated speed of sound. All quantities are calculated over the barotropic slice defined by $\beta$-equilibrium.
• Figure 3: Mass radius relations for cold non-rotating NSs obtained from the sampled models $e_X$. Darker shades indicate a higher $\mathcal{L}_D(X)$. To obtain a readable color map, we use a min–max normalization so that $0\leq \mathcal{L}_D(X) \leq 1$. The best model $e_X$ will therefore have likelihood 1, while models that do not respect the stability-causality requirement have $\mathcal{L}_D(X)=0$ and are not shown. The colored lines represent the metamodel reconstructions in Sec. \ref{['sec_fits']}: FSU2 lies outside of our informed prior because its nuclear matter parameters are outside the range compatible with the $\chi_{EFT}$ constraint discussed in Sec. \ref{['sec_par_space']}.
• Figure 4: Posterior for the dimensionless tidal deformability $\Lambda_X(M)$. The bands show the 68%, 95%, and 99% quantiles for a given mass $M$. The coloured lines denote the $M$-$\Lambda$ relation for the metamodel fits.
• Figure 5: Posterior normalised distributions of the radius, tidal deformability, f-mode frequency for a $1.4 M_\odot$ neutron star with (blue) and without (red) the new NICER results. For comparison, the informed prior distributions are shown in grey. The last panel refers to the distribution of the dUrca threshold mass $M_{dU}$.