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P. A. Gilman, M. Dikpati (HAO/NCAR*)
Gilman & Fox found that latitudinal differential rotation and a broad toroidal field are jointly unstable to 2D horizontal perturbations in the solar tachocline, while each of them is separately stable there. They argued this instability could provide enhanced angular momentum mixing in latitude, as required by Spiegel and Zahn for the solar tachocline to retain its present thickness. Motivated by observations of active regions that imply subsurface toroidal fields of the Sun occur in narrow bands, and assuming that these bands occur in the tachocline at different latitudes as the solar cycle progresses, we examine the joint instability of latitudinal differential rotation and coexisting narrow bands placed at all latitudes. We show that instability occurs for almost all phases of solar cycle, for a wide range of differential rotation amplitudes and toroidal field strengths (between 500 Gauss and 200 kGauss). Mid-latitude bands are most unstable; instability disappears if the band is at very high or low latitudes. We argue that a highly unstable weak (<103 Gauss) high-latitude toroidal band would undergo turbulent mixing in a time short compared to its build-up time due to shearing of poloidal field by differential rotation, and thus may never be buoyant enough to appear as active regions at the surface, providing a possible explanation for why active regions are not seen in high latitudes. Low latitude bands, on the other hand, are unstable with a longer growth time and instability persists for high field strengths (up to 2 x 105 Gauss). Therefore, low-latitude bands can still amplify while experiencing instability, and can still erupt at the surface as active regions. Instability for modes with longitudinal wavenumber m equal to or greater than 1 could help determine the longitude distribution of active regions, and initial nonlinear changes in the toroidal field due to this instability may contribute to their decay.
*The National Center for Atmospheric Research is sponsored by the National Science Foundation.
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