Signature of Phobos’ interior structure in its gravity field and libration

Abstract The interior of the Martian moon Phobos has not been precisely determined yet, in spite of space missions sent at close distance to the body. The current measurements (imagery, astrometric, etc.) lead to controversial conclusions about the level of heterogeneity inside Phobos. Yet, the inside mass distribution is a signature of the conditions prevailing at its formation as well as of its evolution. Here, we study possible heterogenous mass distributions based on internal models built from surface observables and available bulk density and shape measurements. We identify four different families of mass distribution involving rocky material, (macro-)porosity and ice. Mass heterogeneities correspond to either an excess of porosity or a compaction of material under Stickney crater, or a deficit of porosity in the upper layers of Phobos, or a concentration of ice either in depth inside Phobos or in shallow layers. We then discretize the shape of Phobos using 500m-length cubes to fit its volume and total mass. We compute the possible distribution of these cubes for each family of internal mass heterogeneity model. We deduce the possible values of the principal moments of inertia as well as of the geodetic observables such as the libration amplitude and the gravity field anomalies (up to degree and order 10) associated with these models. A comparison of these computed observables between the different heterogeneity models and with their expected homogenous mass distribution values allow us to quantify the possible heterogeneity degree within Phobos. The computed heterogeneity observables can depart by tens of percent from the homogenous values. The most striking departures are from the interior model with mass excess (less porosity) or deficit (more porosity) beneath Stickney crater. In turn, measurements of libration amplitude and low degree coefficients of the gravity field at a precision better than 5% can allow to identify such kinds of heterogeneities mainly located beneath Stickney. Mass excess or deficit can therefore be also distinguished, which is of importance to identify whether Phobos was already porous or monolithic before the formation of Stickney. The current measurements of libration amplitude and degree-two gravity coefficient are quite uncertain, but seem to reject models with higher porosity under Stickney, favoring a pre-impact porous body. The icy models depart less from the homogenous signatures, hence requiring more precise measurements of the geodetic observables and of the shape of Phobos. The improvement of these measurements by the Mars Moon Explorer mission for instance could thus allow for better constraining our model of Phobos’ interior and bring further constraints for its formation.