Neutron Skins and Neutron Stars in the Multimessenger Era

The historical first detection of a binary neutron star merger by the LIGO-Virgo Collaboration [B. P. Abbott et al., Phys. Rev. Lett. 119, 161101 (2017)] is providing fundamental new insights into the astrophysical site for the $r$ process and on the nature of dense matter. A set of realistic models of the equation of state (EOS) that yield an accurate description of the properties of finite nuclei, support neutron stars of two solar masses, and provide a Lorentz covariant extrapolation to dense matter are used to confront its predictions against tidal polarizabilities extracted from the gravitational-wave data. Given the sensitivity of the gravitational-wave signal to the underlying EOS, limits on the tidal polarizability inferred from the observation translate into constraints on the neutron-star radius. Based on these constraints, models that predict a stiff symmetry energy, and thus large stellar radii, can be ruled out. Indeed, we deduce an upper limit on the radius of a $1.4M_{\odot }$ neutron star of $R_{\star }^{1.4}<13.76\mathrm{km}$. Given the sensitivity of the neutron-skin thickness of ${}^{208}\mathrm{Pb}$ to the symmetry energy, albeit at a lower density, we infer a corresponding upper limit of about $R_{\mathrm{skin}}^{208}\lesssim 0.25\mathrm{fm}$. However, if the upcoming PREX-II experiment measures a significantly thicker skin, this may be evidence of a softening of the symmetry energy at high densities—likely indicative of a phase transition in the interior of neutron stars.

Figure 1

The dimensionless tidal polarizability ${\mathrm{\Lambda }}_{\star }^{1.4}$ of a $1.4M_{\odot }$ neutron star as a function of the neutron-skin thickness of ${}^{208}\mathrm{Pb}$ (lower abscissa) and the radius of a $1.4M_{\odot }$ neutron star (upper abscissa) as predicted by the FSUGold2 family of relativistic interactions. Constraints on $R_{\mathrm{skin}}^{208}$ and $R_{\star }^{1.4}$ are inferred from adopting the ${\mathrm{\Lambda }}_{\star }^{1.4}\le 800$ limit deduced from GW170817 [2].

Figure 2

Tidal polarizabilities ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$ associated with the high-mass $M_1$ and low-mass $M_2$ components of the binary predicted by a set of ten distinct RMF models. Models to the right side of the 90% probability contour extracted from Ref. [2] are ruled out. The solid circles represent model predictions for a BNS system having masses of $M_1=1.4M_{\odot }$ and $M_2=1.33M_{\odot }$, respectively.

Figure 3

As in Fig. 1, predictions are shown for ${\mathrm{\Lambda }}_{\star }^{1.4}$ as a function of the radius of a $1.4M_{\odot }$ neutron star and the neutron-skin thickness of ${}^{208}\mathrm{Pb}$, but now for the ten RMF models discussed in the text.

Figure 4

Mass-vs-radius relation predicted by the ten RMF models discussed in the text. Mass constraints obtained from electromagnetic observations of two neutron stars are indicated with a combined uncertainty bar [45, 46]. In contrast, the arrows indicate constraints on stellar radii obtained exclusively from GW170817 and exclude many of the otherwise acceptable EOSs. The excluded causality region was adopted from Fig. 2 of Ref. [55].