A lunar core and the moon's magnetic field

The suggestion that the Moon's magnetic field is due to adiabatic magnetohydrodynamic convection of a molten core has been made by a number of recent authors. Considerations based on petrology, mass and rotational inertia limit the size of this hypothetical core to a few 100 km at the most. A proposal has been made that this core is either molten iron or iron sulfide. Fortunately, we know the properties of both molten iron and iron-sulfide at lunar core pressures. We can find no way of maintaining circulation in a hypothetical lunar core, as circulation is contingent upon a temperature gradient being greater than the adiabatic gradient, or an internal heat source.