Helicity and the solar dynamo

Abstract

The central mechanism in traditional mean-field dynamo theory is the α-effect, and it has been found that the presence of kinetic or magnetic helicities is favourable for the effect, which corresponds to the simultaneous generation of magnetic helicities in the mean field and in the fluctuations, the generation rates being equal in magnitude and opposite in sign. Generally, the two helicities generated by the α-effect, that in the mean field and that in the fluctuations, have either to be dissipated in the generation region or to be transported out of this region. The latter presumably leads to the observed appearance of magnetic helicity in the solar atmosphere, which thus provides valuable information on dynamo processes inaccessible to in situ measurements. We have included details of two numerical dynamo studies in the present review, one for a “laminar” dynamo, where no averaging is applied, the other for a mean-field dynamo. In the first case the full nonlinear system of the incompressible MHD equations is studied in idealized rectangular geometry, with an external forcing of the Roberts type driving a flow in the form of an array of convection-like rolls. Defining mean fields by appropriate averages, it is found that there is a segregation of magnetic helicity between the mean field and the fluctuations similar to that predicted by the mean-field theory of the α-effect. The mean-field calculations are done in a quasi-linear approximation for the turbulence, for realistic spherical geometry, with compressibihy included and using a profile of the solar internal rotation rate obtained from helioseismic inversions. The results are compared with observations, concentrating on the observational finding that the moduli of the averaged values of the force-free twist parameter α ff and and the current helicity H C increase from zero at the equator towards higher latitudes and attain a certain saturation level at middle latitudes (at about 20°–30°). On the assumption that the α-effect is operating in a thin spherical shell, the best coincidence between calculated and observed quantities is found for α-effect operation close to the bottom of the convection zone.