Planetary magnetic fields: A comparative view

Abstract

The sums of the squares of the non-axial (m ≠ 0) spherical-harmonic expansion coefficients (g n m, h n m) yield a readily interpretable exponential spectrum when normalized so as to reflect the global energy content per degree of freedom and plotted against n for each magnetized planet. Indeed, the resulting spectra for Earth, Jupiter, and Uranus suggest an equipartition of magnetic energy among the available degrees of freedom and yield reasonable values for the nominal core radii r c (= 0.432 R E, 0.756 R J, 0.464 R U), which can be interpreted as the mean values of r within the respective fluid cores. Results for Saturn are indeterminate because the most reliable field models are axisymmetric. Results for Mercury are ambiguous because spatial coverage during the Mariner-10 encounters was too limited. Results for Neptune await encounter by Voyager 2. The implications of magnetic-energy equipartition for dynamo theory are unclear but presumably significant, since equipartition seems to suggest the importance of the α-effect (turbulent-eddy formation) for the symmetry-breaking required by Cowling's Theorem in the context of an α-ω dynamo. It seems significant, moreover, that the equatorial projection of the dipole moment belongs to the same exponential spectrum as the analogous projections of the quadrupole and higher moments. If (as seems probable) the spectrum persists during a magnetic reversal (characterized by the condition g 1 0 = 0), then the dipole moment at the time of polarity transition would be perpendicular to the planetary rotation axis and about 20% as strong as the time-averaged moment, which is inclined ∼10° to the rotation axis. Observation of a 58.6° inclination for Uranus' magnetic axis suggests that |g 1 0| is abnormally small at the present epoch (i.e., that Uranus is in the process of undergoing a magnetic reversal). A more usual (∼10°) inclination typical of Earth and Jupiter at times not near polarity transitions would correspond to a dipole moment μ ∼ 1 G-R U 3 and an offset ∼ 0.07 R U for Uranus and (by implication, according to Blackett's Law and similar considerations) a dipole moment μ ∼ 1 G-R N 3 for Neptune.