Rotational stability of dynamic planets with elastic lithospheres

We revisit the classic problem of the secular rotational stability of planets in response to loading using the fluid limit of viscoelastic Love number theory. Gold (1955) and Goldreich and Toomre (1969) considered the stability of a hydrostatic planet subject to an uncompensated surface mass load and concluded that a mass of any size would drive true polar wander (TPW) that ultimately reorients the load to the equator. Willemann (1984) treated the more self-consistent problem where the presence of a lithosphere leads to both imperfect load compensation and a remnant rotational bulge. Willemann considered axisymmetric loads and concluded that the equilibrium pole location was governed by a balance, independent of elastic lithospheric thickness, between the load-induced TPW and stabilization by the remnant bulge. Our new analysis demonstrates that the equilibrium pole position is a function of the lithospheric strength, with a convergence to Willemann's results evident at high values of elastic thickness (>400 km for an application to Mars), and significantly larger predicted TPW for planets with thin lithospheres. Furthermore, we demonstrate that nonaxisymmetric surface mass loads and internal (convective) heterogeneity, even when these are small relative to axisymmetric contributions, can profoundly influence the rotational stability. Indeed, we derive the relatively permissive conditions under which nonaxisymmetric forcing initiates an inertial interchange TPW event (i.e., a 90° pole shift). Finally, Willemann's analysis is often cited to argue for a small (<18°) TPW of Mars driven by the development of a Tharsissized load. We show that even in the absence of the destabilizing effects of load asymmetry, the equations governing rotational stability permit higher excursions of the Martian rotation vector than has previously been appreciated.