Viscosity of Venus' mantle as inferred from its rotational state

Venus' rotation is the slowest of all planetary objects in the solar system and the only one in the retrograde direction. It is commonly admitted that such a rotation state is the result of the balance between the torques created by the gravitational and atmospheric thermal tides1. The internal viscous friction associated with gravitational tides drive the planet into synchronization (deceleration) while the bulge due to atmospheric thermal tides tend to accelerate the planet out of this synchronization1,6. Other torque components (related to the two first one) also affect the rotation2. This work first provide an estimate of the viscosity of Venus' mantle explaining the current balance with thermal atmospheric forcing. Second, this study quantify the impact of the internal structure and its past evolution on the gravitational tides and thus on the rotation history of Venus. Using atmospheric pressure simulations from the Venus climate database4,5,7, we first estimated the atmospheric thermal torque and showed that topography and interior response to atmospheric loading, usually ignored in previous studies, have a strong influence on the amplitude of thermal atmospheric torque. Computing the viscoelastic response of the interior to gravitational tides and atmospheric loading3, we showed that the current viscosity of Venus' mantle must range between 2.3x1020 Pa.s and 2.4x1021 Pa.s to explain the current rotation rate as an equilibrium between torques. We then evaluated the possible past evolution of the viscosity profile of the mantle considering different simple thermal evolution scenarios.  We showed that in absence of additional dissipation processes, viscous friction in the mantle cannot slowdown the rotation to its current state for an initial period shorter than 2-3 days, even for an initially very hot mantle. Beyond Venus, these results has implications for Earth-size exoplanets indicating that their current rotation state could provide key insights on their atmosphere-interior coupling. 1Correia, A. C. M. and J. Laskar (2001), Nature.2Correia, A. C. M. (2003), Journal of Geophysical Research.3Dumoulin, C., G. Tobie, O. Verhoeven, P. Rosenblatt and N. Rambaux (2017), Journal of Geophysical Research.4Lebonnois, S., F. Hourdin, V. Eymet, A. Crespin, R. Fournier and F. Forget (2010),  Journal of Geophysical Research.5Lebonnois, S., N. Sugimoto and G. Gilli (2016), Icarus.6Leconte, J., H. Wu, K. Menou and N. Murray (2015), Science.7Martinez, A., S. Lebonnois, E. Millour, T. Pierron, E. Moisan, G. Gilli and F. Lefèvre (2023), Icarus.