Evolution of the water regime of Phobos

An improved model of the evolution of the water regime of Phobos is presented. The central feature of this model is a time-dependent solar insolation that is influenced both by the increasing solar power output over geologic time and by the obliquity and eccentricity cycles of Mars and Phobos which vary over time scales of 10 ⁵ to 10 ⁶ years. A one-dimensional model is used to calculate temperatures, water fluxes, and ice depths over geologic time. Results are obtained at various latitudes for two assumed cases of porosity and pore size and for three putative values of the mass fraction of water initially allocated to Phobos. Results are obtained for one model that assumes a homogeneous distribution of water ice and for a second model that assumes that water ice is driven toward the surface by the internal thermal gradient near the poles. Results for the (more likely) surface-concentrated model indicate that ice may be found from 270 to 740 m at the equator and from 20 to 60 m at 80° lat depending on porosity and pore size, and subject to limits implied by assumptions of the initial mass fraction of free ice. A two-dimensional model is used to compute temperatures, heat and vapor fluxes, and ice removal/deposition rates for a two-dimensional grid over one obliquity cycle assuming that ice is distributed uniformly throughout Phobos. The heat and vapor fluxes and the ice removal/deposition rates are integrated over time to obtain the water loss at the surface, the lateral heat and vapor transport toward the poles, and the change in ice concentration at interior points. The results show that a relatively large amount of vapor is produced within 1 km of the surface, mostly at lower latitudes. Some of the vapor is transported to the surface where it is lost, and the remainder is transported to greater depths, where it is condensed at much lower rates over a much larger volume. For the large pore size/porosity case, we estimate that the current H ₂O loss rate is ̃3 g/sec. The possible effects of the radiative contributions from Mars, the shadowing by Mars, and the use of an ellipsoidal shape for Phobos are discussed.