Venus' Free Obliquity

The predicted orientation of Venus' rotation axis relative to its orbit can be uniquely determined given knowledge of its J2 gravity coefficient and polar moment of inertia C if its free obliquity is fully damped. This assumption seems warranted given the dominant damping mechanism: turbulent fluid friction at a core mantle boundary (CMB). This skin friction results from differential obliquity of mantle and core spin axes, and the associated damping rate could be as short as 1/106 year. However, the observed pole orientation indicates a free obliquity amplitude ϵ ≃ 2.1° compared with a nominal forced amplitude of 0.5°. There are two plausible explanations. The most likely is that the observed obliquity is a tidally evolved end state in which core friction, modulated by CMB ellipticity and core obliquity amplitude, counterbalances solid and atmospheric tidal torques. This concept is similar to the explanation for the retrograde spin to as an end state in which solid and atmospheric thermal tidal torques balance at the present spin rate because of the ω-1 dependence of the axial thermal torque. Large core ellipticity ec ≡ (Cc - 12(Ac + Bc ))/Cc (Cc ≥ Bc ≥ Ac are core moments of inertia) can substantially increase fluid friction damping time if ec is significantly larger than the whole body ellipticity eo = J2MR2/C ≃ 1.3 × 10-5 by reducing the relative obliquity of core and mantle spin vectors. Note that the hydrostatic contribution to oblateness ∼1.7 × 10-7 is presently negligible. Weaker effects such as solid and thermal tides can then compete with core friction and for plausible models, their sum tends to increase free obliquity. The obliquity balance is controlled by the nonlinear (and nearly quadratic) dependence of the CMB turbulent "skin friction" torque on obliquity. I find that a steady state is achieved for ec ≃ 29eo ≃ 4 × 10-4. If the CMB topography is dynamically supported, then the necessary bottom density anomaly is constrained to the bottom ∼10% of the mantle. An alternative model is that the obliquity results from resonant excitation due to small amplitude (≤0.002°), prograde oscillations in Venus' orbit, one of which happens nearly to match Venus' precession rate σ. This mechanism can account for the obliquity even if the iron core has solidified, but also requires a tectonically quiescent planet (d|J2/dt| < 10-15 year-1). This model has been explored numerically for a wide range of initial conditions, tidal parameters, temporal J2 variations, and chaotic wander of the driving frequencies for the orbit. Only four frequencies, in or near the predicted band for σ, have a significant effect and also have a narrow range of effectiveness. I estimate the polar moment to be in the range 0.0341 ≤ (C/MR2) ≤ 0.331 and hence the precession rate σ to be in the range 44.1 ≤ σ ≤ 45.8″ year-1 based on construction of a suite of density profiles in which mantle composition and core size have theoretically limited variations. Comparing resonance widths to the σ uncertainty, I find that the resonance hypothesis has about a 30% chance of being correct. Core ellipticity also has a profound effect on tidal evolution of Venus obliquity. The ratio of turbulent core and solid tidal friction scales like ω-4, implying that core friction "turns on" only as the spin ω approaches its end state. I also find that the semiannual atmospheric tide can have a dramatic effect on evolution, allowing for inversion of spin orientation from prograde to retrograde if the initial obliquity is sufficiently large (≥45°). Potential measurements which have a bearing on these models including precession rate, tidal Love number k2, and semidiurnal variation in atmospheric pressure at Venus' surface. Perhaps the most useful parameter is k2, which is detectable from orbit, requires only a modest improvement in the tracking accuracy and spacecraft stability over that provided by Magellan, and is an excellent proxy for core fluidity and if fluid, core size and composition.