Solar weak currents, neutrino oscillations, and time variations

The effective neutrino mass in the presence of matter depends on both the charge and three-current weak densities. The effect of solar current loops on neutrino conversion need not be small if the scale of the ``eddies'' is comparable to the local oscillation length. This would seem to offer a mechanism for temporal variations in the neutrino flux that requires neither neutrino magnetic moments nor large solar density fluctuations. The effect of sinusoidally varying currents (or, alternatively, density fluctuations) is explored analytically and numerically. The analytic result we develop is based on the uniform approximation, and reduces to the adiabatic and Landau-Zener results in the appropriate limits. Despite the very interesting effects that may arise, we conclude that this mechanism for temporal variations in the solar-neutrino flux, like others suggested before, appears to require somewhat contrived solar conditions. However, it is quite likely that the influence of currents on neutrino effective masses is important and natural in other astrophysical settings, such as supernovas.