6.5 Is meridional circulation crucial?

The main question regarding meridional circulation is not whether it is there or not, but rather what role it plays in the solar cycle. The answer hinges on the value of the turbulent diffusivity $j T$ , which is notoriously difficult to estimate with confidence. It is probably essential in dynamo models characterized by positive $a$ -effects in the Northern hemisphere, in order to ensure equatorward transport of the sunspot-forming, deep-seated toroidal magnetic field (see Sections 4.4, 4.5, and 4.7). It also appears to be a major determinant in the evolution of the large-scale surface magnetic field in the course of the solar cycle. Something like it is certainly needed in dynamo models based on the Babcock-Leighton mechanism, to carry the poloidal field generated at the surface down to the tachocline, where production of the toroidal field is taking place (see Section 4.8). In the context of Babcock-Leighton models, meridional circulation has also been shown to act as a clock regulating the pace of the solar cycle (Charbonneau and Dikpati, 2000 ), and favoring phase persistence across intermittent, quiescent epochs of suppressed activity (Charbonneau et al., 2004

), in qualitative agreement with inferences from cosmogenic radioisotopes studies.

The primary unknown at this writing is the degree to which meridional circulation is affected by the Lorentz force associated with the dynamo-generated magnetic field. Recent calculations by M. Rempel and collaborators (Rempel, 2004 ) suggest that the backreaction is limited to regions of strongest toroidal fields, so that the “conveyor belt” is still operating in the bulk of the convective envelope. Such calculations must be vigorously pursued.

Another pressing matter is to establish the form and speed of the equatorward return flow in the lower convective envelope, and to determine how much - if any - penetration takes place in the radiative layers below. While Nandy and Choudhuri (2002 ) have argued that deep penetration (i.e., down to $r/R -~ 0.6 o.$ ) is essential for a proper butterfly diagram to be produced, the boundary layer analysis of Gilman and Miesch (2004 ) indicates no significant penetration below the base of the convective envelope. This is an issue where the final word will likely come from helioseismology, hopefully in the not too distant future.