Quadrupole moment of the Sun. Gravitational and rotational potentials

Abstract

Abstract. The solar quadrupole moment J 2 was computed tak-ing into account an up-to-date solar model of mass and density,combined with a recent rotational model established from thehelioseismic data, and including the effects of differential rota-tion with depth. To determine precisely the theoretical value ofJ 2 of the Sun, we integrated the extended differential equationgoverning the fluids in hydrostatic equilibrium, and the Poissonequation for the gravitational potential. From this analysis, wededuced the profiles of J 2 , as a function of the radius and of thelatitude, from the core to the surface. This study has given in-formation on the distortion of the total potential which accountsfor the gravitational and rotational potentials.As a result of our analysis, we found J 2 =1.60.10 −7 whichrespects the upper bound J 2max =3.0.10 −6 derived from thebest knowledge of the Moon’s physical librations. Finally, welinked the profiles of J 2 within the Sun to the solar interiorstructure mainly governed by the shear in the tachocline andjust below the surface.Keywords:Sun:fundamentalparameters–Sun:interior–Sun:rotation – Sun: transition region1. IntroductionThe aim of this study is to investigate the behavior of thequadrupole moment of the Sun, via its gravitational and rota-tional potentials. The shape of the profile of J