The effect of slope distribution on the surface temperature of the moon and other airless bodies

The heat flux experienced by the surface of an airless planetary body is dominated by solar insolation during the day, and by topography at night. Motivated by the close relationship between this heat flux, surface temperature and volatile stability, we consider the effect of the slope distribution on the temperature distribution and hence, prevalence of cold-traps where volatiles may accumulate over geologic time. We present a thermophysical model, accounting for four effects: insolation, reflected and emitted radiation from neighbouring slopes, and subsurface conduction. We investigate specific representative geometries, as well as generic topographies defined by their slope distributions. We find that depressions, such as craters, cast shadows that are more persistent, but warmer than those transiently cast by positive relief features convex in map view, such as hills. We find that while scarce, some briefly illuminated areas may still serve as cold-traps, potentially allowing them to be imaged from orbit. Finally, we estimate the amount of surface and subsurface ice beneath topographies with different roughness and discuss its dependency on latitude.