THE MAGNETIC BODE FALLACY

The magnetic moments and angular momenta of Solar System bodies are co mpared to evaluate the statistical reality of the relation that has co me 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 f ifth power of radius and the magnetic moment the cube. The best fit li ne 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 v alues 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 r epresenting the range of the planet's radii, densities, coefficients o f inertia, periods of rotation, and surface poloidal field intensity. If these variables are considered independent, it was found that the p robability 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 correlation s between the physical parameters besides field, the strong correlatio n with rotation as an important factor in computing the angular moment um is spurious. Comparisons are done using both the angular momenta of the whole planet, and the theorized magnetoactive shells and cores. T he conducting volumes are also compared with the poloidal dipole field s external to these magnetoactive regions. The studies show that the v olumes of the magnetoactive regions appear to be related to the streng th 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 g eometric factor suggested by Runcorn. Plots of field just outside thes e regions versus their volumes show that the Earth and Io have signifi cantly higher fields than those predicted by a line extending from the giant planets to Mercury. Such a Line also does not miss Dolginov's e stimate for Mars by a half order of magnitude. The upper limit of fiel d of Venus falls 3 orders below this trend. If Mars has a core theoriz ed 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 spa cecraft observations is not inconsistent with the trend of the other p lanets. The deviation of Earth and Io from a line joining the other pl anets 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 fre ezing of the inner core whereas for Io the enhancement would be from t idal heating as previously suggested.