Hydrostatic Interfaces in Bodies With Nonhydrostatic Lithospheres

International audience; Below the lithospheres of the terrestrial planets, dwarf planets, and moons, density interfaces adjust over geologic time to align with surfaces of constant gravitational potential. It is well known that the shape of such hydrostatic surfaces is controlled by the pseudo-rotational potential, tidal potential, and the induced potential of nonspherical density interfaces in the body. When a lithosphere is present, however, additional gravitational terms must be considered that arise from, for example, surface relief and crustal thickness variations. A first-order formalism is presented for calculating the shape of hydrostatic density interfaces beneath the lithosphere when the gravity field and surface shape of the body are known. Using an arbitrary discretized density profile, the shapes are obtained by solving a simple matrix equation. As examples, lithospheric gravity anomalies account for about 10% of the relief along hydrostatic interfaces in Mars, whereas for the Moon, the lithospheric gravity is the dominant contributor to the core shape. Spherical harmonic degree-1 mass anomalies in the lithosphere generate degree-1 relief along the core-mantle boundary, and for Mars and the Moon, the core is offset from the center of mass of the body by about 90 m. The moments of inertia of the core of these bodies are also misaligned with respect to the principal moments of the entire body. An improved crustal thickness map of Mars is constructed that accounts for gravity anomalies beneath the lithosphere, and the consequences of core relief on the Martian free core nutation are quantified. Plain Language Summary The shapes of the solid planets and moons are largely hydrostatic and are determined by their rotation rate. If the body has gravity anomalies that arise from within a rigid lithosphere, these will act to perturb the shape of hydrostatic density interfaces beneath the lithosphere, such as the core-mantle boundary. We present a method to compute the shape of density interfaces beneath the lithosphere when the gravity field of the body is known. As examples of our technique, we compute the shape of the core-mantle boundary for Mars and the Moon, both of which are shown to have important contributions that arise from the lithosphere. We also generate a new crustal thickness map that accounts for gravity anomalies generated beneath the lithosphere.