Evolution of Proto-Neutron Stars with Kaon Condensates

We present simulations of the evolution of a proto-neutron star in which kaon-condensed matter might exist, including the effects of finite temperature and trapped neutrinos. The phase transition from pure nucleonic matter to the kaon condensate phase is described using Gibbs' rules for phase equilibrium, which permit the existence of a mixed phase. A general property of neutron stars containing kaon condensates, as well as other forms of strangeness, is that the maximum mass for cold, neutrino-free matter can be less than the maximum mass for matter containing trapped neutrinos or that has a finite entropy. A proto-neutron star formed with a baryon mass exceeding that of the maximum mass of cold, neutrino-free matter is therefore metastable, that is, it will collapse to a black hole at some time during the Kelvin-Helmholtz cooling stage. The effects of kaon condensation on metastable stars are dramatic. In these cases, the neutrino signal from a hypothetical galactic supernova (distance ~8.5 kpc) will stop suddenly, generally at a level above the background in the Super-Kamiokande and Sudbury Neutrino Observatory detectors, which have low-energy thresholds and backgrounds. This is in contrast to the case of a stable star, for which the signal exponentially decays, eventually disappearing into the background. We find the lifetimes of kaon-condensed metastable stars to be restricted to the range of 40-70 s and weakly dependent on the proto-neutron star mass, in sharp contrast to the significantly larger mass dependence and range (1-100 s) of hyperon-rich metastable stars. We find that a unique signature for kaon condensation will be difficult to identify. The formation of the kaon condensate is delayed until the final stages of the Kelvin-Helmholtz epoch, when the neutrino luminosity is relatively small. In stable stars, modulations of the neutrino signal caused by the appearance of the condensate will therefore be too small to be clearly distinguished with current detectors, despite the presence of a first-order phase transition in the core. In metastable stars, the sudden cessation in the neutrino signal occurs whether it is caused by kaon condensation, hyperons, or quarks. However, if the lifetime of the metastable star is less than about 30 s, we find that it is not likely to be due to kaon condensation.