Constraints on radiative decay of the 17-keV neutrino from COBE Measurements

It is shown that, for a nontrivial radiative decay channel of the 17-keV neutrino, the photons would distort the microwave background radiation through ionization of the universe. The constraint on the branching ratio of such decays from COBE measurements is found to be more stringent than that from other considerations. The limit on the branching ratio in terms of the Compton $y$ parameter is $B_\gamma < 1.5 \times 10^{-7} ({\tau_\nu \over 10^{11} sec})^{0.45} ({y \over 10^{-3}})^{1.11} h^{-1}$foran$\Omega=1, \Omega_b=0.1$ universe.