Other
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufmgp23b1010h&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #GP23B-1010
Other
[1510] Geomagnetism And Paleomagnetism / Dynamo: Theories And Simulations, [5734] Planetary Sciences: Fluid Planets / Magnetic Fields And Magnetism
Scientific paper
Based on a new analysis of the differential rotation of the giant planets (which extends into their deep interiors), the magnetic fields of these bodies are most likely to be generated by α-ω dynamos in which the poloidal fields are sheared into large toroidal fields - confined to the electrically conducting region - by the differential rotation (the ω process) and the poloidal field is in turn generated from the toroidal field by small scale, non-axisymmetric motions (the α effect). Since eddy viscosity is the mechanism that draws the differential rotation into the interior, the field strength (B) reaches equilibrium when the magnetic Lorentz force balances the viscous force or when B2 ~ ρνλ/R2, where ρ is the mass density, ν is the kinematic viscosity, λ is the electrical resistivity, and R is the size of the conducting core. In fact, more detailed analysis gives us B2 = (D-Dmin)ρν2/R2, where D is the dynamo number, a dimensionless product of scaled measures of the strengths of the α and ω effects. (Dmin is of order unity for an axisymmetric dipole field and somewhat greater for higher order components.) Conditions in the interiors of Jupiter and Saturn are assumed to be very similar, so the differences in the estimated field strengths are primarily due to geometry (Saturn's smaller size and smaller conducting core). But the observed field strengths of these planets are so disparate that we require D ≤ 2Dmin for Saturn. This small dynamo number leads to very small field strengths for all but the planet's axisymmetric dipole. On the other hand, Jupiter's dynamo number (estimated at D ~ 40Dmin) is large enough to generate many field components (including significant non-axisymmetric dipole and quadrupole components).
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