A fully self-consistent multi-layered model of jupiter
We construct a three-dimensional, fully self-consistent, multi-layered, non-spheroidal model of Jupiter consisting of an inner core, a metallic electrically conducting dynamo region, and an outer molecular electrically insulating envelope. We assume that the Jovian zonal winds are on cylinders parallel to the rotation axis but, due to the effect of magnetic braking, are confined within the outer molecular envelope. We also assume that the location of the molecular-metallic interface is characterized by its equatorial radius HR{sub e}, where R {sub e} is the equatorial radius of Jupiter at the 1 bar pressure level and H is treated as a parameter of the model. We solve the relevant mathematical problem via a perturbation approach. The leading-order problem determines the density, size, and shape of the inner core, the irregular shape of the 1 bar pressure level, and the internal structure of Jupiter that accounts for the full effect of rotational distortion, but without the influence of the zonal winds; the next-order problem determines the variation of the gravitational field solely caused by the effect of the zonal winds on the rotationally distorted non-spheroidal Jupiter. The leading-order solution produces the known mass, the known equatorial and polar radii, and the known zonal gravitational coefficient J {sub 2} of Jupiter within their error bars; it also yields the coefficients J {sub 4} and J {sub 6} within about 5% accuracy, the core equatorial radius 0.09R{sub e} and the core density ρ{sub c}=2.0×10{sup 4} kg m{sup −3} corresponding to 3.73 Earth masses; the next-order solution yields the wind-induced variation of the zonal gravitational coefficients of Jupiter.