Revisiting the determination of solar oblateness from space observations using an optimization method

The Sun is an almost perfect sphere. Its oblateness is about 10^-5 of its radius. Its knowledge can provide strong constraints on solar interior models. The shape of the Sun is depending on the gravitational potential produced by the internal distribution of mass and on centrifugal forces due to the solar rotation. However, due to its very small value, the solar oblateness is very difficult to measure and its determination requires a very good understanding of any possible instrumental effect. Optical effects may distort the image on the CCD and it is not possible to detect the very small difference between the polar and the equatorial radius in a single image. In order to overcome this problem, a distortion mode is implemented. It consists in rotating the satellite by equal angle steps. Once the images have been corrected to all known effects, it is possible to compute the mean solar radius versus the angle on the solar disk averaged over all satellite positions and to fit the results by a sine function to determine the oblateness.

When analysing the solar radius versus angle data, we observe an anticorrelation between the limb brightness and the radius determined from the inflection point. The apparent radius is smaller if an active region is near the limb. The bright active regions are confined to low latitudes and never occur at the poles, which may cause an artefact in the determination of the solar oblateness leading to a negative bias. We developed a new method based on a correction of the solar radius for a given solar angle according to the brightness of the limb at the inflection point and its derivative with radius. This method has been applied to several sequences of SODISM and HMI observations. It provides larger oblateness values than the one based on inflection point, ranging between 8.5 and 9.0 mas for both instruments, in good agreement with the theoretical predictions considering the rotation of the sun. It indicates that the classical method of the inflection point needs to be revisited to take into account the variability of the limb brightness for the determination the solar oblateness.