A novel approach is developed to reconstruct the surface magnetic helicity density for the Sun or sun-like stars. The method is applied on the SDO/HMI-observed vector field synoptic data to study the temporal evolution of the Sun’s magnetic helicity density during Solar Cycle 24.
Power-spectrum analysis is applied on the time-distance measured travel-time shifts in the Sun’s north-south direction along the equatorial area, and the existence of Rossby waves is confirmed.
The Sun’s oblateness shows a variation with solar cycles, in phase with the solar activity level in Cycle 23 but in anti-phase with the activity level in Cycle 24. Such a trend of in-phase during odd cycles and anti-phase during even cycles is confirmed after examining past observations.