Abstract
Jupiter’s dynamo is modelled using the anelastic convection-driven dynamo equations. The reference state model is taken from French et al. [2012]. Astrophys. J. Suppl. 202, 5, (11pp), which used density functional theory to compute the equation of state and the electrical conductivity in Jupiter’s interior. Jupiter’s magnetic field is approximately dipolar, but self-consistent dipolar dynamo models are rather rare when the large variation in density and the effective internal heating are taken into account. Jupiter-like dipolar magnetic fields were found here at small Prandtl number, Pr=0.1. Strong differential rotation in the dynamo region tends to destroy a dominant dipolar component, but when the convection is sufficiently supercritical it generates a strong magnetic field, and the differential rotation in the electrically conducting region is suppressed by the Lorentz force. This allows a magnetic field to develop which is dominated by a steady dipolar component. This suggests that the strong zonal winds seen at Jupiter’s surface cannot penetrate significantly into the dynamo region, which starts approximately 7000km below the surface.
Highlights
Jupiter has the strongest magnetic field of any planet in the Solar System (Connerney, 1993)
The model is based on an equilibrium reference state which uses an equation of state derived from density functional theory, and the electrical conductivity used here is based on ab initio calculations (French et al, 2012)
Since the code we use is pseudospectral, the equilibrium quantities need to be smooth functions, so an interpolating analytic model was used for the reference state density q, temperature T and magnetic diffusivity g 1⁄4 1=l0r where l0 is the permeability of free space and r is the electrical conductivity
Summary
Jupiter has the strongest magnetic field of any planet in the Solar System (Connerney, 1993). Jupiter’s magnetic field is approximately dipolar, but strongly dipolar solutions for anelastic dynamos with large density ratios across the convecting shell are much harder to find (Gastine et al, 2012), a result confirmed here. When the low electrical conductivity region in the non-metallic outer zone is taken into account, dipolar dynamos have been found in Boussinesq (Gómez-Pérez et al, 2010) and polytropic models (Duarte et al, 2013), because the strong convection beyond the transition zone no longer generates disruptive small-scale fields. The recent ab initio calculations (French et al, 2012) suggest the transition zone is further out at $0:9rjup The model has been cut off at r 1⁄4 rcut, 3000 km below the surface, above which the electrical conductivity is essentially zero
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