THE MAGNETIC BODE FALLACY

The magnetic moments and angular momenta of Solar System bodies are compared to evaluate the statistical reality of the relation that has come to be called the ''magnetic Bode law.'' Runcorn has suggested that this ''law'', giving a slope of about 3/5 on a log-log plot, is only a geometrical effect of the angular momenta being proportional to the fifth power of radius and the magnetic moment the cube. The best fit line to the six planets with nonzero magnetic fields is log(m/m(e)) = -0.2(+/-0.2)+0.82(+/-0.05)log(L/L(e)), where the subscripts denote the values for Earth. The value 0.82 is shown to be consistent with the 3/5 slope once estimation bias is accounted for. Monte Carlo analysis was used to construct (2500) synthetic solar systems from the variables representing the range of the planet's radii, densities, coefficients of inertia, periods of rotation, and surface poloidal field intensity. If these variables are considered independent, it was found that the probability of obtaining a slope as different from 0.6 as suggested by Runcorn is 34%, but only a 0.2% chance of obtaining values that are so linear as the actual data on this plot. If instead the covariances of the actual planets are included in the analysis, the mean slope is 0.82 with small deviation, but the odds of obtaining such a tight fit as that observed in the actual Solar System becomes 63%. It is concluded that considering the lack of physical plausibility of the correlations between the physical parameters besides field, the strong correlation with rotation as an important factor in computing the angular momentum is spurious. Comparisons are done using both the angular momenta of the whole planet, and the theorized magnetoactive shells and cores. The conducting volumes are also compared with the poloidal dipole fields external to these magnetoactive regions. The studies show that the volumes of the magnetoactive regions appear to be related to the strength of the poloidal field just outside, and that the tighter trend for the log momentum versus log dipole moment plots is mainly due to the geometric factor suggested by Runcorn. Plots of field just outside these regions versus their volumes show that the Earth and Io have significantly higher fields than those predicted by a line extending from the giant planets to Mercury. Such a Line also does not miss Dolginov's estimate for Mars by a half order of magnitude. The upper limit of field of Venus falls 3 orders below this trend. If Mars has a core theorized to be some 1780 km in radius, a weak dynamo resulting in a surface field close to the limiting 10 - 100 nT range suggested by earlier spacecraft observations is not inconsistent with the trend of the other planets. The deviation of Earth and Io from a line joining the other planets is thought to be due to the added vigor of convection from their extra sources of energy. For Earth this would likely be caused by freezing of the inner core whereas for Io the enhancement would be from tidal heating as previously suggested.