Symmetry energy at supra-saturation densities via the gravitational waves from GW170817

Motivated by the historical detection of gravitational waves from GW170817, the neutron star and the neutron drop, i.e., a certain number of neutrons confined in an external field, are systematically investigated by ab initio calculations as well as the nonrelativistic and relativistic state-of-the-art density functional theories. Strong correlations are found among the neutron star tidal deformability, the neutron star radius, the root-mean-square radii of neutron drops, and the symmetry energies of nuclear matter at supra-saturation densities. For dense matter composed of nucleons only, these correlations, together with the upper limit on the tidal deformability extracted from GW170817, provides the constraints for the neutron star radii, the neutron drop radii, and the symmetry energy at twice saturation density as $R_{1.4M_{\odot }}⩽13.4\pm 0.2\mathrm{km},R_{\mathrm{nd}}⩽2.41\pm 0.10\mathrm{fm}$, and $E_{\mathrm{sym}}\left(2{\rho }_0\right)⩽60.7\pm 10.9\mathrm{MeV}$, respectively.

Figure 1

Tidal deformabilities ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$ associated with the high-mass $M_1$ and low-mass $M_2$ components of the binary neutron star obtained by a set of relativistic (solid lines), nonrelativistic (dashed lines) density functionals, and the results from ab initio RBHF theory using the Bonn potentials and the ab initio variational calculations [Akmal-Pandharipande-Ravenhall (APR)] [43] (dot-dashed lines). The boundary of ${\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_2$ is denoted by the diagonal dotted line. The 90% probability contour is extracted from GW170817 [44].

Figure 2

The tidal deformability ${\mathrm{\Lambda }}_{1.4M_{\odot }}$ of a $1.4\text{−}{M}_{\odot }$ neutron star as a function of the corresponding radius $R_{1.4M_{\odot }}\left(\mathrm{km}\right)$ as predicted by various relativistic (circles) and nonrelativistic (squares) density functionals, in comparison with results calculated by RBHF theory using the Bonn potentials (triangles) and the ab initio variational calculations (APR, diamond). The solid blue curve is the fit to the results of density functionals, and the inner (outer) colored regions depict the 95% confidence (prediction) intervals of the curvilinear regression. The vertical arrow indicates the constraint ${\mathrm{\Lambda }}_{1.4M_{\odot }}⩽720$ [10] from GW170817, which leads to $R_{1.4M_{\odot }}⩽13.4\pm 0.2\mathrm{km}$ labeled by the horizontal arrow according to the correlations.

Figure 3

The radius of a $1.4\text{−}{M}_{\odot }$ neutron star against the rms radius $R_{\mathrm{nd}}$ for $N=20$ neutrons trapped in a harmonic-oscillator (HO) potential ($\hslash \omega =25\mathrm{MeV}$) obtained with various relativistic (circles) and nonrelativistic (squares) density functionals as well as the RBHF theory using the Bonn potentials (triangles). The solid blue line is a linear fit to the results of density functionals. The upper limit $R_{1.4M_{\odot }}⩽13.4\pm 0.2\mathrm{km}$ deduced from Fig. 2 is shown with the vertical arrow, which gives a constraint $R_{\mathrm{nd}}⩽2.41\pm 0.10\mathrm{fm}$ labeled by the horizontal arrow.

Figure 4

Correlations between the symmetry energy of nuclear matter at twice nuclear saturation density and rms radii of 20 neutrons in a HO with $\hslash \omega =25\mathrm{MeV}$, calculated by relativistic (circles), nonrelativistic (squares) density functional theories, and ab initio methods (triangles). The upper limit $R_{\mathrm{nd}}⩽2.41\pm 0.10\mathrm{fm}$ deduced from the correlations between $R_{1.4M_{\odot }}$ vs $R_{\mathrm{nd}}$ is shown with the horizontal arrow, which gives rise to an upper limit $E_{\mathrm{sym}}\left(2{\rho }_0\right)⩽60.7\pm 10.9\mathrm{MeV}$ labeled by the vertical arrow.