  We show that in a supernova core the longitudinal photon (plasmon) has a
space-like dispersion and Cerenkov absorption and emission of such photons is
kinematically allowed. If the neutrino has a non-zero magnetic moment, then
helicity flipping Cerenkov absorption of a plasmon $\nu_L+\gamma\to\nu_R$ is
the most efficient cooling mechanism of the supernova core, and this allows us
to put a restrictive bound on the neutrino magnetic moment
$\mu_{\nu}~<~0.7\times 10^{-13}\mu_B$.
