We use a simple analytic model to examine the effect of the atmospheric source properties on the spatial distribution of a volatile in a surface-bounded atmosphere on a satellite that is tidally-locked to its planet. Spatial asymmetries in the O2 exosphere of Europa observed using the Hubble Space Telescope appear to reveal on average a dusk enhancement in the near-surface ultraviolet auroral emissions. Since the hop distances in these ballistic atmospheres are small, we use a 1-D mass conservation equation to estimate the latitudinally-averaged column densities produced by suggested O2 sources. Although spatial asymmetries in the plasma flow and in the surface properties certainly affect the spatial distribution of the near-surface aurora, the dusk enhancements at Europa can be understood using a relatively simple thermally-dependent source. Such a source is consistent with the fact that radiolytically produced O2 permeates their porous regoliths and is not so sensitive to the local production rate from ice. The size of the shift towards dusk is determined by the ratio of the rotation rate and atmospheric loss rate. A thermally-dependent source emanating from a large reservoir of O2 permeating Europa's icy regolith is consistent with the suggestion that its subsurface ocean might be oxidized by subduction of such radiolytic products.