A new estimate of the quadrupole moment of the sun

Recent solar observations at Pic du Midi are reported that yield a value of J ₂=(2.57 ± 2.36) x 10^–6 for the quadrupole moment of the Sun. These observations were conducted from July 1993 to July 1994 after several improvements of the scanning heliometer. This instrument operates by fast photoelectric scans of opposite limbs of the Sun quasi-simultaneously, which provides the distance between both inflection points of the limb profiles. Any number of solar diameters in any position angle can be measured within a time interval short enough to minimize the scattering of the observational parameters. Errors due to atmospheric deterioration are discussed. From our results, compared to previous values obtained by other authors, it can be concluded than an upper limit for J ₂ is probably 1.0 × 10^-5.     

Observations of the Solar Limb Shape Distortions

Two new campaigns devoted to the observation of the solar limb distortions were made at the Pic-du-Midi Observatory, in September 2000 and September 2001, by means of the scanning heliometer. This apparatus can be used now routinely to accurately determine solar limb profiles (at two wavelengths), at any heliographic latitudes. Each measurement is made within 44 milliseconds (of time) which permits to record a limb profile together with the seeing. Scans are automatically rejected for seeing larger than 1.3 arc sec. Such conditions are essential to perform high-quality observations necessary to obtain the quadrupole term (l=2) in the polynomial expansion of the radius contour R() _{= constant} = R ₀ left(1+_l c _l P _l()right). Exceptional meteorological conditions in September 2001 (seeing of the order of 18 cm, for a 50 cm clear aperture of the refractor) enabled us to determine c ₂ and c ₄ (see Table I) with an accuracy of a few milli-arc-sec. Results indicate a distorted solar shape, the departures from a pure spherical body not exceeding 20 milli-arc-sec. We propose a model to interpret such results (the combination of a nearly uniform rotating core with a prolate solar tachocline and an oblate surface), which is briefly discussed. Our results are confronted to those obtained from space. We conclude that measurements of the quadrupole term from the ground are possible, but of high difficulty and can be obtained only during excellent weather conditions. The hexadecapole term should be only obtained from space. We show that an astrometric satellite would be required, whose mission would be also to accurately determine the solar rotation profiles (both surface and in depth) in order to unambiguously determine the inertia moments of the Sun through the J _n terms. Such values are also briefly discussed.