Potential Effects of Atmospheric Collapse on Martian Heat Flow and Application to the InSight Measurements

Heat flow is an important constraint on planetary formation and evolution. It has been suggested that Martian obliquity cycles might cause periodic collapses in atmospheric pressure, leading to corresponding decreases in regolith thermal conductivity (which is controlled by gas in the pore spaces). Geothermal heat would then build up in the subsurface, potentially affecting present-day heat flow - and thus the measurements made by a heat-flow probe such as the InSight HP$^{3}$ instrument. To gauge the order of magnitude of this effect, we model the diffusion of a putative heat pulse caused by thermal conductivity changes with a simple numerical scheme and compare it to the heat-flow perturbations caused by other effects. We find that an atmospheric collapse to 300 Pa in the last 40 kyr would lead to a present-day heat flow that is up to $2-8\%$ larger than the average geothermal background. Considering the InSight mission with expected $5-15\%$ error bars on the HP$^{3}$ measurement, this perturbation would only be significant in the best-case scenario of full instrument deployment, completed measurement campaign, and a well-modelled surface configuration. The prospects for detecting long-term climate perturbations via spacecraft heat-flow experiments remain challenging.