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Session 2 - Everything Else.
Display session, Friday, June 27
Ballroom C, Chair: Richard Canfield

[2.12] Joint Instability of Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone, II

P. A. Gilman, P. Fox (HAO/NCAR)

At the 1996 AAS/SPD meeting in Madison we reported first results for the joint instability of differential rotation and toroidal magnetic fields to 2D disturbances (see also Gilman and Fox, Paper I, July 20 1997 issue of ApJ). This analysis was for the toroidal field profile B=a*sin(LAT)cos(LAT). This paper reports results for the profile B=(a*sin(LAT)+b*(sin(LAT))^3))cos(LAT), which, with b<-a<0, allows for a node in the toroidal field at latitude arcsin (-a/b). This generalization is of interest because we should expect such a node to appear and migrate equatorward as the sun proceeds from one sunspot cycle to the next. As with the simpler profile, instability occurs for virtually all differential rotation amplitudes, and all toroidal field amplitudes and shapes, and remains confined to disturbances with longitudinal wave number m=1. For a, b>0, the instability is enhanced for the same a compared to the b=0 case, particularly in high latitudes. For 0>b>-a (so no node is present) the instability is similar to the b=0 case but with diminished growth rates, due to the reduction of toroidal fields at high latitudes. At b=-a, the symmetric mode of instability vanishes, but the antisymmetric mode remains. For b<-a<0, both symmetric and antisymmetric modes are unstable, but with disturbances confined largely to the domain poleward of the node, unless the toroidal field energy greatly exceeds the kinetic energy of differential rotation. Unstable disturbances spread and migrate toward the equator as the field strength is increased and as the node is moved equatorward. Thus, the instability may still contribute to the existence of the solar butterfly diagram, and to other solar dynamo presses.

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