A convection zone dynamo including the effects of magnetic buoyancy and downward flows

Abstract

A magnetic flux tube may be considered both as a separate body and as a confined field. As a field, it is affected both by the cyclonic convection ($α$-effect) and differential rotation ($Ω$-effect). As a body, the tube experiences not only a buoyant force, but also a dynamic pressure due to downflows above the tube. When these two dynamic effects are incorporated into the $αΩ$ dynamo equations, we obtain a dynamo operating in the convection zone. We analyze and solve the extended dynamo equations in the linear approximation by using observed solar internal rotation and assuming a downflow suggested by numerical simulations of the solar convection zone. The results produce: (i) the 22-year cycle period; (ii) the extended butterfly diagram; (iii) the confinement of strong activity to low heliographic latitudes $|Φ|\le 35^\circ$; (iv) at low latitudes the radial field is in an approximately $π$ phase lag compared to the toroidal field at the same latitude; (v) the poleward branch is in a $π/2$ phase lag with respect to the equatorward branch; (vi) most of the magnetic flux is present in a strongly intermittent form, concentraed into strong flux tubes; (vii) the magnetic field peaks at a depth of $r=0.96 R_{\sun}$; (viii) total solar irradiance varies in phase with the solar cycle activity, having an amplitude of 0.1%; (ix) solar effective temperature varies in phase with the solar cycle activity, having an amplitude of 1.5 $^\circ C$; and (x) solar radius also varies in phase with the solar cycle activity, having an amplitude of 20 mas. All these results are in agreement with the corresponding observations.