Solar cycle variations of rotation and asphericity in the near-surface shear layer

Abstract The precise shape of the Sun is sensitive to the influence of gravity, differential rotation, local turbulence and magnetic fields. So its precise measurement is a long-standing astrometric objective. It has been previously shown by different methods that the solar shape exhibits asphericity that evolves with the solar cycle. Thanks to the Michelson Doppler Imager (MDI) on Solar and Heliospheric Observatory (SoHO) and the Helioseismic and Magnetic Imager (HMI) aboard NASA's Solar Dynamics Observatory (SDO), and their capability to observe with an unprecedented accuracy the surface gravity oscillation (f) modes, it is possible to extract information concerning the coefficients of rotational frequency splitting, a 1 , a 3 and a 5 , that measure the latitudinal differential rotation, together with the a 2 , a 4 and a 6 asphericity coefficients. Analysis of these helioseismology data with time for almost two solar cycles, from 1996 to 2017, reveals a close correlation of the a 1 and a 5 coefficients with the solar activity, whilst a 3 exhibits a long-term trend and a weak correlation with the solar activity in the current solar cycle indicating a substantial change of the global solar rotation, potentially associated with a long-term evolution of the solar cycles. Looking in more details, the asphericity coefficients, a 2 , a 4 and a 6 are more strongly associated with the solar cycle when applying a time lag of respectively 0.1, 1.6 and −1.6 years. The magnitude of a 6 -coefficient varies in phase with the sunspot number (SN), but its amplitude is ahead of the SN variation. The latest measurements made in mid 2017 indicate that the magnitude of the a 6 -coefficient has probably reached its minimum; therefore, the next solar minimum can be expected by the end of 2018 or in the beginning of 2019. The so-called “seismic radius” in the range of f-mode angular degree: l = 137 − 299 exhibits a temporal variability in anti-phase with the solar activity; its relative value decreased by ∼ 2.3 × 10 − 5 in Solar Cycle 23 and ∼ 1.7 × 10 − 5 in Cycle 24. Such results will be useful for better understanding the physical mechanisms which act inside the Sun, and so, better constrain dynamo models for forecasting the solar cycles.