Outgassing on Stagnant-Lid Planets: Influence of Rheology
Authors: Tackley Paul 
Published: March 2024

Outgassing from the interior is a key process influencing the evolution of the atmospheres of rocky planets. For planets with a stagnant lid tectonic mode, previous models have indicated that increasing planet size very strongly reduces the amount of outgassing, even to zero above a certain planet mass (Dorn et al., A&amp;A 2018). This is because melt is buoyant only above a certain depth, which becomes shallower with increasing planet size (hence "g"); for large enough planets this depth may even lie within the lithosphere, preventing eruption and outgassing.&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; However, uncertainties in rheology strongly influence the temperature structure of planets, hence (i) the depth at which melt is generated and (ii) the thickness of the lithosphere. One major uncertainty is the rheology of post-perovskite, which constitutes a large fraction of the mantle in large super-Earths. Ammann et al. (Nature 2010) find that diffusion is anisotropic; it is not clear whether the "upper bound" or "lower bound" is relevant to large-scale deformation, but both result in high viscosity at very high pressures, strongly influencing the radial temperature profile (Tackley et al., Icarus 2013). In contrast, Karato (2011, Icarus) argues that a different mechanism - interstitial diffusion - acts to make viscosity almost independent of pressure and relatively low in the post-perovskite regime.&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; Another uncertainty is the reference viscosity (the viscosity at a reference temperature, pressure and stress), as this depends on bulk composition, water content, grain size and other properties. Lower reference viscosity results in thinner lithosphere and crust (e.g., Armann &amp; Tackley, JGR 2012).&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; Thus, numerical simulations are performed of the long-term (10 Gyr) thermo-chemical evolution of stagnant-lid planets (coupled mantle and core) with masses between 1 to 10 Earth masses, varying the reference viscosity and the rheology of post-perovskite. The simulations are based on the setup of Tackley et al. (2013 Icarus) with the addition of partial melting and basaltic crustal production, and outgassing of a passive tracer that partitions into the melt and outgasses 100% upon eruption.&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; Results indicate that:the previously-found trend of lower percentage outgassing with larger planet size is reproduced, but
outgassing does not fall to zero even in a 10 Earth mass planet. Outgassing of between 15% and 70% is found for 10 Earth mass planets (up to ~100% for Earth mass planets).
Post-perovskite rheology (interstitial, lower-bound or upper-bound) makes only a minor difference to long-term outgassing, but does influence the timing of outgassing.
Reference viscosity makes a large difference to outgassing, with lower viscosities leading to substantially larger outgassing percentages.
Internal heating plays a major role: stagnant-lid planets initially heat up due to low heat transfer efficiency, thinning the lithosphere and producing widespread melting.