Neutron Stars. II. Neutrino-Cooling and Observability

Calculations of the rates of the cooling reactions $n+n\to n+p+e^{-}+{\nu }_e$ and $n+{\pi }^{-}\to n+e^{-}+{\nu }_e$ are presented; the rates of the closely related muon-producing reactions and the four inverse processes are also given. Several different arguments are used to obtain estimates of the relavant matrix elements. The nucleons are assumed to form a normal Fermi fluid with a continuous excitation spectrum. The calculated cooling rates indicate that a neutron star containing quasifree pions would cool within a few days to a temperature so low that the star would be unobservable. The surface of a star that does not contain quasifree pions would cool to ${10}^7$ °K in a few months and would reach 4×${10}^6$ °K in about 100 years. The calculated cooling rates strongly indicate that the discrete x-ray sources located in the direction of the galactic center are not neutron stars.