A Systematic Study of Hale and Anti-Hale Sunspot Physical Parameters

We present a systematic study of sunspot physical parameters using full-disk magnetograms from the Michelson Doppler Imager/Solar and Heliospheric Observatory and the Helioseismic and Magnetic Imager/Solar Dynamic Observatory. Our aim is to use uniform data sets and analysis procedures to characterize the sunspots, paying particular attention to the differences and similarities between Hale and anti-Hale spots. Included are measurements of the magnetic tilt angles, areas, fluxes, and polarity pole separations for 4385 sunspot groups in Cycles 23 and 24 each measured, on average, at similar to 66 epochs centered on meridian crossing. The sunspots are classified as either Hale or anti-Hale, depending on whether their polarities align or anti-align with Hale's hemispheric polarity rule. We find that (1) the anti-Hale sunspots constitute a fraction (8.1 +/- 0.4)% of all sunspots, and this fraction is the same in both hemispheres and cycles; (2) Hale sunspots obey Joy's law in both hemispheres and cycles but anti-Hale sunspots do not-three equivalent forms of Joy's law are derived: sin gamma = (0.38 +/- 0.05) sin phi, gamma = (0.39 +/- 0.06) phi, and gamma = (23.80 +/- 3.51) sin phi, where gamma is the tilt angle and phi is the heliospheric latitude; (3) the average Hale sunspot tilt angle is (gamma) over bar = 5 degrees.49 +/- 0.09; and (4) the tilt angles, magnetic fluxes, and pole separations of sunspots are interrelated, with larger fluxes correlated with larger pole separations and smaller tilt angles. We present empirical relations between these quantities. Cycle 24 is a much weaker cycle than Cycle 23 in sunspot numbers, cumulative magnetic flux, and average sunspot magnetic flux. The anti-Hale sunspots are also much weaker than Hale sunspots in those parameters, but they share similar magnetic flux distributions and average latitudes. We characterize the two populations, and aim to shed light on the origin of anti-Hale sunspots.