Effects of weak interaction on kaon condensation and cooling of neutron stars

Abstract

Kaon condensation and its implication in the cooling mechanism in neutron stars are investigated within a framework of current algebra and PCAC. The weak interaction, n ⇌ p + K −, is shown to play a significant role in determining not only the critical density but also the equation of state of the K − condensed phase. The chemical equilibrium for the weak interaction leads to large proton-admixture. In connection with this result, the possibility of the direct URCA process, n → p + e − + v ̄ e , p + e − → n + v e , is investigated. It is shown that, within a simple treatment without the nuclear interactions such as the symmetry energy, the kinematical condition for the direct URCA process is not satisfied despite the large proton-mixing, due to the resulting small electron Fermi momentum. The physical content of the K − condensation from a viewpoint of strangeness degrees of freedom is also discussed.