Neutron Stars. II. Neutrino-Cooling and Observability

Abstract

Calculations of the rates of the cooling reactions $n+n\ensuremath{\rightarrow}n+p+{e}^{\ensuremath{-}}+{\ensuremath{\nu}}_{e}$ and $n+{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}n+{e}^{\ensuremath{-}}+{\ensuremath{\nu}}_{e}$ 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 ${10}^{7}$ \ifmmode^\circ\else\textdegree\fi{}K in a few months and would reach 4\ifmmode\times\else\texttimes\fi{}${10}^{6}$ \ifmmode^\circ\else\textdegree\fi{}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.