Evolution of proto-neutron stars with kaon condensates

We present simulations of the evolution of a proto-neutron star in which ka on-condensed matter might exist, including the effects of finite temperatur e and trapped neutrinos. The phase transition from pure nucleonic matter to the kaon condensate phase is described using Gibbs' rules for phase equili brium, which permit the existence of a mixed phase. A general property of n eutron stars containing kaon condensates, as well as other forms of strange ness, is that the maximum mass for cold, neutrino-free matter can be less t han the maximum mass for matter containing trapped neutrinos or that has a finite entropy. A proto-neutron star formed with a baryon mass exceeding th at of the maximum mass of cold, neutrino-free matter is therefore metastabl e, 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 st ars are dramatic. In these cases, the neutrino signal from a hypothetical g alactic supernova (distance similar to8.5 kpc) will stop suddenly, generall y at a level above the background in the Super-Kamiokande and Sudbury Neutr ino Observatory detectors, which have low-energy thresholds and backgrounds . This is in contrast to the case of a stable star, for which the signal ex ponentially decays, eventually disappearing into the background. We find th e lifetimes of kaon-condensed metastable stars to be restricted to the rang e 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 co ndensation will be difficult to identify. The formation of the kaon condens ate is delayed until the final stages of the Kelvin-Helmholtz epoch, when t he neutrino luminosity is relatively small. In stable stars, modulations of the neutrino signal caused by the appearance of the condensate will theref ore be too small to be clearly distinguished with current detectors, despit e 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 ca used 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.