Parity properties of an advection-dominated solar $α^2\Om$-dynamo

Abstract

We have developed a high-precision code which solves the kinematic dynamo problem both for given rotation law and meridional flow in the case of a low eddy diffusivity of the order of $10^{11}$ cm$^2$/s known from the sunspot decay. All our models work with an \alf-effect which is positive (negative) in the northern (southern) hemisphere. It is concentrated in radial layers located either at the top or at the bottom of the convection zone. We have also considered an \alf-effect uniformly distributed in all the convection zone. In the present paper the main attention is focused on i) the parity of the solution, ii) the form of the butterfly diagram and iii) the phase relation of the resulting field components. If the helioseismologically derived internal solar rotation law is considered, a model without meridional flow of high magnetic Reynolds number (corresponding to low eddy diffusivity) fails in all the three issues in comparison with the observations. However, a meridional flow with equatorial drift at the bottom of the convection zone of few meters by second can indeed enforce the equatorward migration of the toroidal magnetic field belts similar to the observed butterfly diagram but, the solution has only a dipolar parity if the (positive) \alf-effect is located at the base of the convection zone rather than at the top. We can, therefore, confirm the main results of a similar study by Dikpati & Gilman (2001).