Third family of superdense stars in the presence of antikaon condensates

The formation of K^- and K⁰ condensation in β-equilibrated hyperonic matter is investigated within a relativistic mean field model. In this model, baryon-baryon and (anti)kaon-baryon interactions are mediated by the exchange of mesons. It is found that antikaon condensation is not only sensitive to the equation of state but also to the antikaon optical potential depth. For large values of the antikaon optical potential depth, K^- condensation sets in before the appearance of negatively charged hyperons. We treat K^- condensation as a first-order phase transition. The Gibbs criteria and global charge conservation laws are used to describe the mixed phase. Nucleons and Λ hyperons behave dynamically in the mixed phase. A second-order phase transition to K⁰ condensation occurs in the pure K^- condensed phase. Along with K^- condensation, K⁰ condensation makes the equation of state softer, thus resulting in smaller maximum mass stars compared with the case without any condensate. This equation of state also leads to a stable sequence of compact stars called the third family branch, beyond the neutron star branch. The compact stars in the third family branch have different compositions and smaller radii than that of the neutron star branch.