The solar oblateness and its relationship with the structure of the tachocline and of the Sun's subsurface

The solar oblateness was computed with a dynami- cal up-to-date solar model of mass and density, combined with a recent rotational model established from the helioseismic data, and including the effects of differential rotation with depth. To determine the theoretical value of the oblateness of the Sun, we integrated the extended differential equation governing the fluids in hydrostatic equilibrium and the Poisson equation for the gravitational potential. From this analysis, we deduced the profiles of as a function of the radius and of the latitude, from the core to the surface, for a Sun splitted into a series of con- centric shells. As each shell is affected by a potential distortion, mainly due to the rotation, and as the rotation rate depends on the radius and on the latitude, each shell of the Sun is affected by a different oblateness. As a result of the integration of this function, we found =8 :77:10 6 , that we compared to the oblateness of a rigidly rotating sphere. To interprete the difference in oblateness of the studied layers within the Sun, we linked the profiles to the solar interior structures, specially to the tachocline and to the subsurface, that help us to understand why and how these regions are mainly governed by shear. In particular, we propose for these two layers a double structure, one where the magnetic field would be stored and one of shear. Finally, we compared our results of radial integrated oblate- ness with the latitudinal variation of the semidiameter from solar astrolabe observations.