  To ascertain whether magnetic dynamos operate in rocky exoplanets more
massive or hotter than the Earth, we developed a parametric model of a
differentiated rocky planet and its thermal evolution. Our model reproduces the
established properties of Earth's interior and magnetic field at the present
time. When applied to Venus, assuming that planet lacks plate tectonics and has
a dehydrated mantle with an elevated viscosity, the model shows that the dynamo
shuts down or never operated. Our model predicts that at a fixed planet mass,
dynamo history is sensitive to core size, but not to the initial inventory of
long-lived, heat-producing radionuclides. It predicts that rocky planets larger
than 2.5 Earth masses will not develop inner cores because the
temperature-pressure slope of the iron solidus becomes flatter than that of the
core adiabat. Instead, iron "snow" will condense near or at the top of these
cores, and the net transfer of latent heat upwards will suppress convection and
a dynamo. More massive planets can have anemic dynamos due to core cooling, but
only if they have mobile lids (plate tectonics). The lifetime of these dynamos
is shorter with increasing planet mass but longer with higher surface
temperature. Massive Venus-like planets with stagnant lids and more viscous
mantles will lack dynamos altogether. We identify two alternative sources of
magnetic fields on rocky planets: eddy currents induced in the hot or molten
upper layers of planets on very short period orbits, and dynamos in the ionic
conducting layers of "ocean" planets with ~10% mass in an upper mantle of water
(ice).
