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The modeling of the quadrupole moment J 2 and of the oblateness e, two key solar parameters, derives from the development in successive spherical harmonics of the gravitational potential. These harmonics are representative of the shape of the Sun, by studying the local distortion of the internal layers, under their distribution of mass and velocity. The first aim of this paper is to study, over the radius r and the colatitude θ, the structure of the internal layers of the Sun through a geometrical approach, considering J 2 and e under a differential form. The second aim is to determine their theoretical values, after integration over r and θ, taking the best available models of density and rotation into account constrained by helioseismic data. The novelty of our approach lies in the analysis of the profiles of the two above-mentioned solar parameters, under differential form, from the core to the surface. This analysis allows us to comply with the physical processes located in the transition regions, namely the tachocline and maybe a new subsurface layer which could be called the leptocline. The profiles of tildeJ 2 show two sharp decreases, which are directly connected to the shear layers located at 0.7 R ⊙ and beneath the surface. The profiles of tildee show five changes of curvature, which seem to be connected to solar processes, such as the matter circulation flows, seismic events or the storage of the magnetic field, phenomena taking place in the transition regions. These sets of profiles allow us to propose a configuration scenario composed of a double layer. Moreover, as a result of the theoretical determination of tildeJ 2 and tildee, the values at the surface of the quadrupole moment and of the oblateness can be deduced, which are 1.60×10−7 and 8.77×10−6, respectively. As a result of an analysis of available data, we may admit J 2=(2.0±0.4)×10−7. The theoretical computations of J 2 and e at the surface will be confronted in the near future with the values measured in space by means of the Picard microsatellite. This mission should permit one to measure at the same time both the total solar irradiance and the latitudinal diameters in any position angle (after removing the passing spots or faculae at the limb). |
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