Recovering Joy's Law as a Function of Solar Cycle, Hemisphere, and Longitude

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. Mt. Wilson Observatory data from 1917 - 1985 are used to analyze the active-region tilt angle as a function of solar cycle, hemisphere, and longitude, in addition to the more common dependence on latitude. Our main results are as follows: i) 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. ii) We determine that the hemispheric mean tilt value of active regions varies with each solar cycle, although the noise from a stochastic process dominates and does not allow for a determination of the slope of Joy's law on an 11-year time scale. iii) The hemispheric difference in mean tilt angles, 1.1^∘±0.27, over Cycles 16 to 21 was significant to a three-σ level, with average tilt angles in the Northern and Southern hemispheres of 4.7^∘±0.26 and 3.6^∘±0.27, respectively. iv) Area-weighted mean tilt angles normalized by latitude for Cycles 15 to 21 anticorrelate with cycle strength for the southern hemisphere and whole-Sun data, confirming previous results by Dasi-Espuig et al. (Astron. Astrophys.518, A7, 2010). The Northern Hemispheric mean tilt angles do not show a dependence on cycle strength. v) Mean tilt angles do not show a dependence on longitude for any hemisphere or cycle. In addition, the standard deviation of the mean tilt is 29 - 31^∘ for all cycles and hemispheres, indicating that the scatter is due to the same consistent process even if the mean tilt angles vary.