Session 69 - The Solar Dynamo and Helioseismology.
Display session, Thursday, June 13
Tripp Commons,

## [69.02] Nonlinear interface dynamos with \alpha-quenching

P. Charbonneau, K. B. MacGregor (HAO, NCAR)

There exist various mechanisms capable of limiting the magnitude of the (presumably) dynamo-generated, large-scale solar magnetic field. One such mechanism is the so-called \alpha-quenching''. The underlying idea is that the Lorentz force associated with the dynamo-generated magnetic fields impedes the small scale, turbulent fluid motions giving rise to the so-called \alpha-effect'' (the production of poloidal from toroidal fields in the framework of mean-field dynamo theory). In mean-field models, a popular ---yet essentially ad hoc--- prescription for \alpha-quenching consists in replacing the coefficient (\alpha) of the \alpha-effect source term in the dynamo equations by an expression of the form \alpha\to \alpha(B) =\alpha_0/(1+(|B|/B_eq)^2), where \alpha_0 is a measure of the strength of the \alpha-effect in the linear regime, and B_eq is the equipartition field strength, based on the kinetic energy of the turbulent, convective fluid motions (B_eq\sim 10^4\,G at the base of the solar convection zone). In principle, such Weak Quenching'' allows the production of magnetic fields of roughly equipartition strength, as demonstrated by the numerous conventional mean-field dynamo models making use of eq. , or some close variant, published to date. Vainshtein amp; Cattaneo (1992, ApJ 393, 165) and Gruzinov amp; Diamond (1995, Phys. Plasmas 2, 1941) have argued, however, that \alpha-quenching should be described by \alpha\to \alpha(B) =\alpha_0/(R_m(|B|/B_eq)^2) where R_m is a magnetic Reynolds number based on the microscopic properties of the flow (R_m\gg 1 for solar interior conditions). This now describes a much stronger form of \alpha-quenching, and, with R_m\gg 1, could be fatal to large-scale dynamo action, in the sense that the dynamo could only produce magnetic fields of strength \ll B_eq. This is in marked contradiction with the demands set by recent models of bipolar magnetic region emergence, which require field strengths of order 10\times B_eq\sim 10^5\,G for the observed latitudes and tilt of emergence to be adequately reproduced.

In this contribution, we investigate the circumstances under which interface dynamos can avoid \alpha-quenching, either in the Weak'' or Strong'' forms defined above. In interface dynamos the \alpha-effect is assumed to operate within the solar convective envelope, while the strongest magnetic fields are generated by shearing below the core-envelope interface (Parker 1993, ApJ 408, 707; Charbonneau amp; MacGregor, submitted to ApJ). This spatial segregation of the \alpha-effect source region is the key to avoiding \alpha-quenching. This is illustrated using a few nonlinear, kinematic interface dynamo solutions applicable to the Sun.