Neutron-star radii based on realistic nuclear interactions

The existence of neutron stars with $2M_{\odot }$ requires strong stiffness of the equation of state (EoS) of neutron-star matter. We introduce a multi-Pomeron exchange potential (MPP) working universally among three- and four-baryon systems to stiffen the EoS. Its strength is restricted by analyzing the nucleus-nucleus scattering with the $G$-matrix folding model. The EoSs are derived using the Brueckner-Hartree-Fock (BHF) theory and the cluster variational method (CVM) with the nuclear interactions ESC and AV18. The mass-radius relations are derived by solving the Tolmann-Oppenheimer-Volkoff (TOV) equation, where the maximum masses over $2M_{\odot }$ are obtained on the basis of terrestrial data. Neutron-star radii $R$ at a typical mass $1.5M_{\odot }$ are predicted to be $12.3\text{–}13.1$ km. The uncertainty of calculated radii is mainly from the ratio of three- and four-Pomeron coupling constants, which cannot be fixed by any terrestrial experiment. Though values of $R\left(1.5M_{\odot }\right)$ are not influenced by hyperon-mixing effects, finely observed values for them indicate degrees of EoS softening by hyperon mixing in the region of $M\sim 2M_{\odot }$. If $R\left(1.5M_{\odot }\right)$ is less than about 12.3 km, the softening of EoS by hyperon mixing has to be weak. Useful information can be expected by the space mission NICER, offering precise measurements for neutron-star radii within $\pm 5\%$.

Figure 1

Differential cross sections for ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ elastic scattering at $E_{\mathrm{in}}/A=70$ MeV calculated with $G$-matrix folding potentials. Solid, dashed, and dot-dashed curves are for ESC+MPa, AV18+MPa, and $\mathrm{AV}18+{\mathrm{MPa}}^{\prime }$, respectively. Dotted curves are for ESC and AV18.

Figure 2

Energy per particle $E/A$ as a function of nucleon density $\rho$ symmetric matter. Solid curves in the left (right) panel are obtained by ESC+MPa and ESC+MPb ($\mathrm{AV}18+{\mathrm{MPa}}^{\prime }$ and $\mathrm{AV}18+{\mathrm{MPb}}^{\prime }$), and the dot-dashed one is by ESC (AV18). The box shows the empirical value.

Figure 3

Neutron-star masses as a function of the radius $R$. Solid, dashed, and dotted curves are for ESC+MPa, ESC+${\mathrm{MPa}}^{+}$ and ESC+MPb, respectively. The dot-dashed curve is for ESC. The upper two dotted horizontal lines show the observed masses $1.97M_{\odot }$ and $2.01M_{\odot }$ of $\mathrm{J}1614-2230$ and J0348+0432, respectively. The lower dotted line shows the mass $1.5M_{\odot }$ of a typical neutron star.

Figure 4

Neutron-star masses as a function of the radius $R$. Solid curves are for ESC+MPa and ESC+MPb. Dashed curves are for $\mathrm{AV}18+{\mathrm{MPa}}^{\prime }$ and $\mathrm{AV}18+{\mathrm{MPb}}^{\prime }$. Also see the caption of Fig. 3.

Figure 5

$E/A$ curves of symmetric and pure neutron matter. Solid and dashed curves are for $\mathrm{AV}18+{\mathrm{MPa}}^{\prime }$ and $\mathrm{AV}18+{\mathrm{MPb}}^{\prime }$, respectively. Thick (thin) curves are obtained by CVM (BHF).

Figure 6

$MR$ curves of neutron stars for $\mathrm{AV}18+{\mathrm{MPa}}^{\prime }$ and $\mathrm{AV}18+{\mathrm{MPb}}^{\prime }$. Solid and dashed curves are obtained by CVM and BHF, respectively. Also see the caption of Fig. 3.

Figure 7

Neutron-star masses as a function of the radius $R$. Solid (dashed) curves are with (without) hyperon ($\mathrm{\Lambda }$ and ${\mathrm{\Sigma }}^{-}$) mixing for ESC+MPa and ESC+MPb. The dot-dashed curve for MPb is with $\mathrm{\Lambda }$ mixing only. Also see the caption of Fig. 3.