Hyperon stars in the Brueckner-Bethe-Goldstone theory

In the framework of the Brueckner-Bethe-Goldstone theory, we determine a fully microscopic equation of state for asymmetric and $\ensuremath{\beta}$-stable nuclear matter containing ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ and $\ensuremath{\Lambda}$ hyperons. We use the Paris and the new Argonne ${\mathrm{Av}}_{18}$ two-body nucleon interaction, whereas the nucleon-hyperon interaction is described by the Njimegen soft-core model. We stress the role played by the three-body nucleon interaction, which produces a strong repulsion at high densities. This enhances enormously the hyperon population, and produces a strong softening of the equation of state, which turns out almost independent on the nucleon-nucleon interaction. We use the new equation of state in order to calculate the structure of static neutron stars. We obtain a maximum mass configuration with ${M}_{\mathrm{max}}=1.26$ (1.22) when the Paris ${(Av}_{18})$ nucleon potential is adopted. Central densities are about 10 times normal nuclear matter density. Stellar rotations, treated within a perturbative approach, increase the value of the limiting mass by about 12%.