Joy’s Law, Anti-Hale classifications, and the evolution of emerging sunspot regions

This thesis aims to use analysis of the time dependence of sunspot locations and other physical characteristics to provide an improved empirical basis for understanding solar magnetic fields. Bipolar active regions in both hemispheres tend to be tilted with respect to the East–West Equator of the Sun in accordance with Joy’s law, which describes the average tilt angle as a function of latitude. We recommend a revision of Joy’s law towards a weaker dependence on latitude (slope of 0.13–0.26) and without forcing the tilt to zero at the Equator. We determine that the hemispheric mean tilt value of active regions varies with each solar cycle but mean tilt angles do not show a dependence on longitude for any hemisphere or cycle. We also explore the visual representation of magnetic tilt angles on a traditional butterfly diagram to show that the average latitude of anti-Hale regions does not differ from the average latitude of all regions in both hemispheres. The distribution of anti-Hale sunspot tilt angles is broadly distributed between 0 and 360° with a weak preference for east-west alignment 180° from their expected Joy’s law angle. Anti-Hale sunspots display a log-normal size distribution similar to that of all sunspots, indicating no preferred size for anti-Hale spots. In addition, we report that 8.4%±0.8% of all bipolar sunspot regions are misclassified as Hale in traditional catalogues. This percentage is slightly higher for groups within 5° of the Equator due to the misalignment of the magnetic and heliographic equators. We also investigate bipolar sunspot regions and how tilt angle and footpoint separation vary during emergence and decay, finding that within ±48 hours of the time of peak umbral area, large regions steadily increase in tilt angle, midsize regions are nearly constant, and small regions show evidence of negative tilt during emergence. A period of growth in footpoint separation occurs over a 72-hour period for all of the regions from roughly 40 to 70 Mm. The smallest bipoles are outliers in that they do not obey Joy’s law and have a much smaller footpoint separation. We confirm previous research that the sunspots appear to be two distinct populations, where the smallest spots are potentially supergranular precursors to the more familiar flux tube sunspots. In summary, this thesis has revealed increased complexity in sunspot behavior compared to previous studies and demonstrates that analysis of sunspot observations continues to provide an empirical basis for improved models of small-scale solar flux tubes and the underlying magnetic dynamo.