Recovering Solar Toroidal Field Dynamics from Sunspot Location Patterns

Abstract

We analyze both Kitt Peak magnetogram data and MDI continuum intensity sunspot data to search for the following solar toroidal band properties: width in latitude and the existence of a tipping instability (longitudinal m ¼1 mode) for any time during the solar cycle. In order to determine the extent to which we can recover the toroidal field dynamics, we forward-model artificially generated sunspot distributions from subsurface toroidal fields that we have assigned certain properties. Sine-curve fitting of Kitt Peak magnetogram data provided an upper limit of 15 to the tipping amplitude but could not adequately separate the tip from the width of the toroidal band. We then analyzed two sunspot distribution parameters using MDI and model data: the average latitudinal separation of sunspot pairs as a function of longitudinal separation and the number of sunspot pairs creating a given angle with respect to the east-west direction. A toroidal band of 10 width with a constant tipping of 5 best fitsMDI data early in the solar cycle, when the sunspot band is at high latitudes (>18N5). A toroidal band of 20 width with a tipping amplitude decreasing in time from 5 to 0 best fits MDI data late in the solar cycle when the sunspot band is at low latitudes (<18N5).Model data generated by untipped toroidal bands cannot fitMDI high-latitude data using 2 goodness-of-fit criteria and can fit only one sunspot distribution parameter at low latitudes. Tipped toroidal bands satisfy 2 criteria at both high and low latitudes for both sunspot distribution parameters. We conclude that this is evidence to reject the null hypothesis—that toroidal bands in the solar tachocline do not experience a tipping instability—in favor of the hypothesis that the toroidal band experiences an m ¼1 tipping instability for a significant portion of the solar cycle. Our finding that the band widens from10 early in the solar cycle to 20 late in the solar cycle may be explained in theory by magnetic drag spreading the toroidal band due to altered flow along the tipped field lines. Higher m modes, most notably m ¼ 2 and 6, are apparent in MDI data, but further analysis is needed to determine this property in detail.