Hyperon mixing and universal many-body repulsion in neutron stars

A multi-Pomeron exchange potential (MPP) is proposed as a model for the universal many-body repulsion in baryonic systems on the basis of the extended soft core (ESC) baryon-baryon interaction. The strength of the MPP is determined by analyzing the nucleus-nucleus scattering with the $G$-matrix folding model. The interaction in $\Lambda N$ channels is shown to reproduce well the experimental $\Lambda$ binding energies. The equation of state (EoS) in neutron matter with hyperon mixing is obtained including the MPP contribution, and mass-radius relations of neutron stars are derived. It is shown that the maximum mass can be larger than the observed one, $2M_{\odot }$, even in the case of including hyperon mixing on the basis of model parameters determined by terrestrial experiments.

Figure 1

Differential cross sections for ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ elastic scattering at $E/A=70$ MeV calculated with the $G$-matrix folding potentials. Solid, dashed, and dot-dashed curves are for MPa, MPb, and MPc, respectively. The dotted curve is for ESC.

Figure 2

Double-folding potentials for ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ elastic scattering at $E/A=70$ MeV. Solid, dashed, and dot-dashed curves are for MPa, MPb, and MPc, respectively. The dotted curve is for ESC.

Figure 3

Energy spectra of $\Lambda$ hypernuclei (${}_{\Lambda }{}^{13}\mathrm{C}$, ${}_{\Lambda }^{28}\mathrm{Si}$, ${}_{\Lambda }{}^{51}\mathrm{V}$, ${}_{\Lambda }^{139}\mathrm{La}$, ${}_{\Lambda }^{208}\mathrm{Pb}$) derived from MPa (solid lines) and ESC (dotted lines). Experimental values are marked by open circles.

Figure 4

$U_{\Lambda }^{\left(n\right)}$ for ${\rho }_{\Lambda }/{\rho }_n=0.2$ as a function of ${\rho }_n$. Solid, dashed, dot-dashed, and dotted curves are for MPa, MPb, MPc, and ESC, respectively.

Figure 5

$U_{{\Sigma }^{-}}^{\left(n\right)}$ for ${\rho }_{\Sigma }/{\rho }_n=0.2$ as a function of ${\rho }_n$. Also see the caption of Fig. 4.

Figure 6

Square and circle marks are calculated values of $E_N$ with MPa for symmetric and neutron matter, respectively. Fitting functions are shown by solid curves.

Figure 7

Calculated values of $E_{\Lambda }$ with MPa in the $n+\Lambda$ case. Square, circle, and triangle marks are for $x_{\Lambda }=0.1,0.2,0.3$, respectively. Fitting functions are shown by solid curves.

Figure 8

Composition of hyperonic neutron-star matter in the case of MPa.

Figure 9

Composition of hyperonic neutron-star matter in the case of ESC.

Figure 10

Pressure $P$ as a function of energy density $\varepsilon$ in the cases of MPa (upper curves) and ESC (lower curves). Solid and dotted curves are with and without hyperon mixing, respectively. In the dashed curve with hyperon mixing, MPP + TBA parts are switched off in channels including hyperons.

Figure 11

Pressure $P$ as a function of baryon density ${\rho }_B$ in the cases of MPa (upper curves) and ESC (lower curves). Also see the caption of Fig. 10.

Figure 12

Neutron-star masses as a function of the radius $R$. Solid, dashed, dot-dashed, and dotted curves are for MPa/b/c and ESC, respectively.

Figure 13

Neutron-star masses as a function of the radius $R$. Dashed and dotted curves are obtained from MPa and ESC, respectively, without hyperon mixing. The solid (dot-dashed) curve is obtained with hyperon mixing, where MPP contributions are included in all baryons universally (only in nucleon sectors).

Figure 14

Neutron-star masses as a function of the central density ${\rho }_c$. Also see the caption of Fig. 13.