Implications of PREX-2 on the Equation of State of Neutron-Rich Matter

Laboratory experiments sensitive to the equation of state of neutron rich matter in the vicinity of nuclear saturation density provide the first rung in a “density ladder” that connects terrestrial experiments to astronomical observations. In this context, the neutron skin thickness of ${}^{208}\mathrm{Pb}$ ($R_{\mathrm{skin}}^{208}$) provides a stringent laboratory constraint on the density dependence of the symmetry energy. In turn, an improved value of $R_{\mathrm{skin}}^{208}$ has been reported recently by the PREX collaboration. Exploiting the strong correlation between $R_{\mathrm{skin}}^{208}$ and the slope of the symmetry energy $L$ within a specific class of relativistic energy density functionals, we report a value of $L=(106\pm 37)\mathrm{MeV}$—which systematically overestimates current limits based on both theoretical approaches and experimental measurements. The impact of such a stiff symmetry energy on some critical neutron-star observables is also examined.

Figure 1

Left: slope of the symmetry energy at nuclear saturation density ${\rho }_0$ (blue upper line) and at $(2/3){\rho }_0$ (green lower line) as a function of $R_{\mathrm{skin}}^{208}$. The numbers next to the lines denote values for the correlation coefficients. Right: Gaussian probability distribution for the slope of the symmetry energy $L=L({\rho }_0)$ inferred by combining the linear correlation in the left figure with the recently reported PREX-2 limit. The six error bars are constraints on $L$ obtained by using different theoretical approaches [14, 19, 20, 21, 22, 23, 24, 25].

Figure 2

Constraints on the $J\text{−}L$ correlation obtained from a variety of experimental and theoretical approaches. The figure was adapted from Refs. [20, 33] and noticeably displays the tension with the recent PREX-2 result.

Figure 3

Direct Urca thresholds for the onset of enhanced cooling in neutron stars. The threshold density is depicted by the lower blue line and the corresponding stellar mass for such a central density with the upper green line. The shaded area represents PREX-2 $1\sigma$ confidence region. For each of these two quantities, the best-fit line is displayed together with their associated correlation coefficients.

Figure 4

Showcase of neutron star observables as a function of $R_{\mathrm{skin}}^{208}$ as predicted by the set of energy density functionals considered in this work. The tidal deformability ${\mathrm{\Lambda }}_{\star }^{1.4}$ of a $1.4{\mathrm{M}}_{\odot }$ neutron star is computed for each model, and displayed with blue dots and connected by a best fit power law that scales as the $4.8\approx 5$ power of $R_{\star }^{1.4}$. The combined PREX-2 result together with NICER constraints on the stellar radius is depicted by the small (blue) window of models allowed.