Recovering Solar Toroidal Field Dynamics From Sunspot Location Patterns
  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=1 mode) for any time during the solar cycle. To determine the extent which we can recover the toroidal field dynamics, we forward model artificially generated sunspot distributions from subsurface toroidal fields we assigned certain properties. We 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 E-W direction. A toroidal band of 10 degrees width with a constant tipping of 5 degrees best fits MDI data early in the solar cycle. A toroidal band of 20 degrees width with a tipping amplitude decreasing in time from 5 to 0 degrees best fits MDI data late in the solar cycle. Model data generated by untipped toroidal bands cannot fit MDI high latitude data and can fit only one parameter at low latitudes. Tipped toroidal bands satisfy chi squared criteria at both high and low latitudes. We conclude 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=1 tipping instability. Our finding that the band widens from ~10 degrees early in the solar cycle to ~20 degrees 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. 
Aimee A. Norton and Peter A. Gilman