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We investigate the neutrino helicity-flip process under supernova coreconditions, where the left-handed neutrinos being produced can be convertedinto right-handed neutrinos sterile with respect to the weak interaction due tothe interaction of magnetic moments with plasma electrons and protons. Insteadof the uniform ball model for the SN core used in previous analyses, realisticmodels for radial distributions and time evolution of physical parameters inthe supernova core are considered. We have obtained new upper limits on theDirac neutrino magnetic moment averaged over flavours and time from thecondition that the influence of the right-handed neutrino emission on the totalcooling time scale should be limited.

Reexamination of a Bound on the Dirac Neutrino Magnetic Moment from the Supernova Neutrino Luminosity