Magnetic field strength estimations for the main phases of solar cycles 13-24 using magnetohydrodynamic Rossby waves in the lower tachocline

Abstract

The magnetic field strength (MFS) estimates used by the existing space weather prediction models (SWPMs) are inaccurate. Consequently, it has been indicated that there is a need to find solutions to rectify the wrong assumption that the magnetic field remains constant in strength and location throughout the solar cycle. This study explores a solution to this problem by increasing the granularity and accuracy of the previous MFS estimations by calculating them for the main phases of the solar cycle (solar minimum and maximum) per hemisphere for solar cycles 13-24. A dispersion relation of the fast magnetohydrodynamic (MHD) Rossby wave was derived analytically in spherical coordinates that included a toroidal magnetic field and latitudinal differential rotation, which adequately captures the dynamics of the lower tachocline. Secondly, a change to the methodology of calculating the MFS that utilises the established connection between the observed Rieger-type periodicity (RTP) in solar activity of 150-190 days and the fast MHD Rossby wave in the lower tachocline was proposed. Furthermore, a new magnetic field profile (MFP) of Bφ = B0 sin(6Θ) was introduced to improve the model results. This MFP has a maximum and minimum value at the same latitudes associated with sunspot appearances during these extreme solar cycle phases. Consequently, the MFS values were calculated at a latitude of 29◦ (solar min) and 16◦ (solar max) using the hemispheric RTP data. The average MFS (RTP) for the solar min and solar max in the dominant hemisphere was established to be 8 kG (212 days) and 76 kG (163 days), respectively. For the non-dominant hemisphere, the average MFS was established to be 5 kG (213 days) and 50 kG (183 days) for the solar min and max, respectively. The results of this study show a significant difference in the results based on latitude. The findings have also revealed that the periodicity of increased solar activity associated with a specific MFS is affected not only by the solar cycle strength and hemispheric asymmetry but also by the solar cycle phase (or latitude) considered. Additionally, we strongly argue that this study’s MFS results represent reality more closely than previously calculated results. Therefore, we propose that the MFS estimates reported in this study should be considered for the input to various existing space weather prediction models.