Crustal remanence in an internally magnetized non-uniform shell: a possible source for Mercury's magnetic field?
We consider the magnetic field of a shell uniformly magnetized by an internal dipole that is subsequently removed. The Gauss coefficients of the resulting field are given in terms of the spherical harmonic coefficients of the shell thickness. This general solution can easily be reduced to common special cases by superposition. For a shell of constant thickness the external field vanishes (by Runcorn's theorem). For shell thickness variations caused by a laterally varying temperature field, the resulting magnetic moments are appreciably greater than the previously published correction due to rotational flattening. If the crust of Mercury contains rocks capable of sustaining high specific magnetizations, orif Mercury had a now-extinct dynamo field which was more intense than the Earth's present core field, then the Mariner 10 observations of Mercury's magnetic field are consistent in magnitude and geometry with the predictions of this model. For such a scenario, the requirement of a fractionally large molten outer core supporting a dynamo at present would be relaxed. The origin of Mercury's magnetic field will be addressed with measurements to be made by NASA's MESSENGER spacecraft.