A NEW SOLAR-CYCLE MODEL INCLUDING MERIDIONAL CIRCULATION

We present a kinematic model for the solar cycle which includes not only the transport of magnetic flux by supergranular diffusion and a poleward bulk flow at the Sun's surface, but also the effects of turbulent diffusion and an equatorward "return flow" beneath the surface. As in the earlier models of Babcock and Leighton, the rotational shearing of a subsurface poloidal field generates toroidal flux that erupts at the surface in the form of bipolar magnetic regions (BMRs). However, such eruptions do not result in any net loss of toroidal flux from the Sun (as assumed by Babcock and Leighton); instead, the large-scale toroidal field is destroyed both by "unwinding" as the local poloidal field reverses its polarity, and by diffusion as the toroidal flux is transported equatorward by the subsurface flow and merged with its opposite hemisphere counterpart. The inclusion of meridional circulation allows stable oscillations of the magnetic field, accompanied by the equatorward progression of flux eruptions, to be achieved even in the absence of a radial gradient in the angular velocity. We describe an illustrative case in which a subsurface flow speed of order 1 m s-1 and subsurface diffusion rate of order 10 km2 s-1 yield 22 yr oscillations in qualitative agreement with observations.