Excitation of Tumbling in Phobos and Deimos.

Mass-spring model simulations are used to investigate past spin states of a viscoelastic Phobos and Deimos. From an initially tidally locked state, we find crossing of a spin-orbit resonance with Mars or a mean motion resonance with each other does not excite tumbling in Phobos or Deimos. However, once tumbling our simulations show that these moons can remain so for an extended period and during this time their orbital eccentricity can be substantially reduced. We attribute the tendency for simulations of an initially tumbling viscoelastic body to drop into spin-synchronous state at very low eccentricity to the insensitivity of the tumbling chaotic zone volume to eccentricity. After a tumbling body enters the spin synchronous resonance, it can exhibit long lived non-principal axis rotation and this too can prolong the period of time with enhanced tidally generated energy dissipation. The low orbital eccentricities of Phobos and Deimos could in part be due to spin excitation by nearly catastrophic impacts rather than tidal evolution following orbital resonance excitation.