Solar shape variations across cycles 24 and 25: Observations from 2010 to 2023

The longest continuous time-series of solar oblateness measurements, initiated in 2010 and still ongoing, has been obtained from data collected by the Helioseismic Magnetic Imager (HMI) aboard NASA's Solar Dynamics Observatory (SDO). Based on HMI data, we developed two methods for determining the solar oblateness at 617.33\\,nm in the continuum .\nThe first method involves determining solar oblateness using HMI solar disk images and limb observations from twenty-three SDO satellite roll calibration maneuvers between 2010 and 2023 .\nThrough meticulous analysis of these observation sequences, we obtained a precise measurement of solar oblateness using this technique, yielding a value of 9.02 (pm 0.72)times 10$^ $ (6.28pm 0.50\\,kilometers), unaffected by brightness contamination from sunspots and magnetically induced excess emission. We also verified the polarization independence of light, showing consistent HMI solar oblateness measurements across Stokes states. Interestingly, our solar oblateness time-series, based on HMI solar disk images and limb observations, seems to be in anti-phase with solar activity. The second method we used relies on determining solar oblateness from HMI helioseismic inference of internal rotation. With this approach, we obtained a solar oblateness of 8.40 (pm 0.02)times 10$^ $ (5.85pm 0.01 kilometers) with a variation in phase with solar activity (0.05times 10$^ $ (0.04\\,kilometers at 1\\,sigma ) over an 11--year sunspot cycle). This outcome is troubling as it conflicts with our results obtained from the HMI solar limb observations