Modeling the Internal Structure of Mars Using Normal Mode Relaxation Theory

We seek to resolve an apparent paradox between two sets of observations, which seem to suggest quite different thermal structures for the deep interior of Mars. The orbit of Phobos is observed to be accelerating along-track at a rate of (273.4 ± 1.2) 10^(-5) deg/yr^(2), which implies that the orbit is shrinking at (4.03 ± 0.03) cm/yr, and losing energy at a rate of 3.4 MW. The most likely sink for that energy is tidal dissipation within Mars, seemingly requiring a warm interior. However, static support of the gravity and topography of Mars requires a thick elastic lithosphere, indicating a relatively cool (and therefore stiff) mantle. Using normal mode relaxation theory we model the internal viscosity structure of Mars by analyzing its response to tidal forcing from Phobos. We investigate spherical axisymmetric layered viscoelastic models, seeking to satisfy what is known about planetary differentiation, to support large-scale topography via a thick elastic lithosphere, and to yield the observed tidal dissipation rate. We present a family of 4-layer models (core, mantle, lithosphere, and thin weak layer) that satisfy these constraints, and discuss the implications for Mars’ internal structure.