JOINT INSTABILITY OF LATITUDINAL DIFFERENTIAL ROTATION AND CONCENTRATED TOROIDAL FIELDS BELOW THE SOLAR CONVECTION ZONE

摘要

Motivated by observations of sunspot and active-region latitudes that suggest that the subsurface toroidal field in the Sun occurs in narrow latitude belts, we analyze the joint instability of solar latitudenal differential rotation and the concentrated toroidal field below the base of the convection zone, extending the work of Gilman $ Fox (hereafter GF). We represent the profile of the toroidal field by Gaussian functions whose width is a variable parameter and solve the two-dimensional perturbation equations of GF by relaxation methods. We reproduce the results of GF for broad profiles, and we find instability for a wide range of amplitudes of differential ratation and toroidal fields, (10(3) - 10(6)G fields at the base of the solar convection zone), as well as a wide range of toroidal-field bandwidths. We show that the combination of concentrated toroidal fields and solar-type latitudinal differential rotation is again unstable, not only to longitudinal wavenumber m=1 as in GF, but also to m>1 for sufficiently norrow toroidal-field profiles. For a fixed peak field strength, the growth rate first increases as the toroidal-field band is narrowed, reaching a peak for bandwidths between 10 degrees and 20 degrees in latitude, depending on the peak field strength, and then decreases to cut-off in the instability for toroidal field bands of 3 degree - 4 degree. Irrespective of bandwidth, the differental rotation is the primary energy source for the instability for weak fields, and the toroidal field is the primary source for which the toroidal field becomes the primary energy