Solar oblateness and its variations in phase with the 22 yr magnetic cycle

HMI (Helioseismic and Magnetic Imager) Science NuggetThe internal dynamics of the Sun is manifested by disturbances on the photosphere surface, inducing directly small deviations from its sphericity. The solar shape then reflects the internal state of the Sun and processes taking place herein. Its temporal variations are useful for modelling the Sun, particularly in relation to its activity cycle. The solar oblateness i.e. Pole-Equator radius difference, is therefore a key input for models. Oblateness measurements since the beginning of the 20th century are still very controversial. Many measurements were carried out, raising questions about its average value and its temporal variations. Gravitational models and helioseismology, giving access to radial profiles of latitudinal differential rotation and the internal magnetic field, have identified acceptable values of oblateness, mostly induced by the centrifugal force on superficial layers with a weak contribution of the gravitational quadrupole moment J 2. Modern oblateness measurements confirmed expected values. Time series recorded from the ground, balloons, and lately Space showed variations but they were inconclusive. They were in phase or in anti-phase with solar activity while others reported no obvious variations [1]. Oblateness measurements obtained from HMI are therefore a major asset for explaining those of the past and the inconsistencies reported since they now cover almost an entire cycle. Solar oblateness is computed from images recorded during roll procedures, i.e. the calibration mode of SDO where the spacecraft is rotated around HMI line-of-sight. The roll procedure is run twice a year with solar images recorded in the continuum near the Fe I absorption line (617.3 nm) in a narrow band (70 mA). The processing method is explained with Figure 1. It allows estimating the solar shape that is fitted with Legendre polynomials up to the fourth order. The dimensionless distortion coefficients C 2 (quadrupole) and C 4 (hexadecapole) are thus estimated, which makes it possible to deduce solar oblateness. Roll sequences, ran between October 2010 and July 2018, resulted in an average solar oblateness of 8.8 ± 0.8 mas (6.4 ± 0.6 km), in good agreement with measurements of the last two decades and consistent with helioseismology-based models. Time variations were observed and appear in anti-phase with Cycle 24 sunspot number taken as proxy of solar activity (Fig. 2). C 2 variations are in phase with activity while C 4 presents anti-symmetric variations with respect to the maximum solar activity time. The oblateness measurement