The Dependence of Joy’s Law and Mean Tilt as a Function of Flux Emergence Phase

Abstract

Data from the Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI) are analyzed from 1996 to 2023 to investigate tilt angles ( γ ) of bipolar magnetic regions and Joy’s law for Solar Cycles 23 and 24 and a portion of Cycle 25. The HMI radial magnetic field ( B _r ) and MDI magnetogram ( B _los ) data are used to calculate ( γ ) using the flux-weighted centroids of the positive and negative polarities. Each active region (AR) is only sampled once. The analysis includes only Beta ( β )-class ARs since computing γ of complex ARs is less meaningful. During the emergence of the ARs, we find that the average tilt angle ( $\bar{\gamma }$ ) increases from 3.°30 ± 0.75 when 20% of the flux has emerged to 6.°79° ± 0.66 when the ARs are at their maximum flux. Cycle 24 has a larger average tilt, ${\bar{\gamma }}_{24}$ =6.67 ± 0.66, than Cycle 23, ${\bar{\gamma }}_{23}$ = 5.11 ± 0.61. No significant difference is found in the slope of Joy’s law or $\bar{\gamma }$ when sampling the ARs at the time of maximum flux or central meridian crossing. There are persistent differences in $\bar{\gamma }$ in the hemispheres, with the Sun's southern hemisphere having higher $\bar{\gamma }$ in Cycles 23 and 24, but the uncertainties are such that these differences are not statistically significant.

Keywords

• Sunspots
• Solar dynamo
• Solar cycle