Magnetic field-minimum intensity correlation in sunspots: A tool for solar dynamo diagnostics

Within a sunspot umbra, the continuum intensity is known to be inversely proportional to the magnetic field strength. Studied less is the relationship between the minimum continuum intensity and the maximum field strength of different sunspots. We conduct a test of this global relationship, using brightness ratios and magnetic field data from the Advanced Stokes Polarimeter and the Michelson Doppler Imager (MDI) for 10 sunspot umbrae of various sizes observed 1998 May - 2003 June. We determine that the peak field strengths of sunspots can be ascertained from a fit to their corresponding brightness ratios with an accuracy of approximate to 100 G, nearly twice the accuracy that a fit to the MDI magnetogram values can provide. We then analyze continuum intensity data from the MDI to characterize the distribution of sunspots as a function of latitude. We hand-select 331 and 321 umbrae, respectively, in the northern and southern hemispheres during Carrington rotations 1910 - 2003. Although the average location of sunspot eruption moves equatorward throughout the solar cycle, the northern hemisphere shows darker umbrae located systematically closer to the equator, while brighter umbrae are found at higher latitudes. These findings confirm the results of simulations that show strong flux emerging radially while weak flux emerges nonradially, causing weak flux to emerge poleward of its original toroidal field position. The average umbral intensity decreased in the north through the solar cycle, reaching a minimum intensity around sunspot maximum, possible evidence of the toroidal field strength peaking at solar maximum. This finding is in opposition to previous observations suggesting an increase late in the cycle. The southern hemisphere umbral distribution appears more disorganized and periodic in nature.