Equilibrium rotational stability and figure of Mars

Studies extending over three decades have concluded that the current orientation of the martian rotation pole is unstable. Specifically, the gravitational figure of the planet, after correction for a hydrostatic form, has been interpreted to indicate that the rotation pole should move easily between the present position and a site on the current equator, 90° from the location of the massive Tharsis volcanic province. We demonstrate, using general physical arguments supported by a fluid Love number analysis, that the so-called non-hydrostatic theory is an inaccurate framework for analyzing the rotational stability of planets, such as Mars, that are characterized by long-term elastic strength within the lithosphere. In this case, the appropriate correction to the gravitational figure is the equilibrium rotating form achieved when the elastic lithospheric shell (of some thickness LT) is accounted for. Moreover, the current rotation vector of Mars is shown to be stable when the correct non-equilibrium theory is adopted using values consistent with recent, independent estimates of LT. Finally, we compare observational constraints on the figure of Mars with non-equilibrium predictions based on a large suite of possible Tharsis-driven true polar wander (TPW) scenarios. We conclude, in contrast to recent comparisons of this type based on a non-hydrostatic theory, that the reorientation of the pole associated with the development of Tharsis was likely less than 15° and that the thickness of the elastic lithosphere at the time of Tharsis formation was at least ∼ 50   km. Larger Tharsis-driven TPW is possible if the present-day gravitational form of the planet at degree 2 has significant contributions from non-Tharsis loads; in this case, the most plausible source would be internal heterogeneities linked to convection.