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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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