Efficient tidal dissipation in Deimos

Abstract

After its formation Deimos, Mars' second and outer satellite, is expected to have been catastrophically disrupted, possibly multiple times, by planetesimals left over from primary terrestrial planet accretion. The expected last time such a disruption occurred is ca. 4.3 Gyr ago. After this disruption and its subsequent expected coagulation from a thin circum-martian ring, Deimos likely experienced a gradual excitation in its orbital eccentricity from flybys with other leftover planetesimals. The cumulative effect from these encounters indicates that Deimos' eccentricity should have been up to an order of magnitude greater than it is now, with a mean value of 1.5−1.1+2.3×10−3. Based on this eccentricity excitation, Deimos' calculated age, the assumption of synchronous rotation throughout its existence and that the eccentricity is only tidally damped in Deimos and not in Mars, the resulting tidal parameters of Deimos are k2D/QD=3.52−2.89+2.04 × 10−5 (2σ). The large uncertainties in the tidal parameters are caused by the wide eccentricity distribution resulting from encounters with stray planetesimals. Employing a simple tidal model, I calculate that Deimos' shear viscosity is ηD=2.13−0.79+9.77×1012 Pa s, far lower than that of cold rock. Under the assumption that Deimos' interior is akin to a rubble pile its internal rigidity is μrp ~ 120 MPa, while the tidal Love number falls in the range k2D ~ (1 − 7) × 10−5. The low rigidity and viscosity indicate that most of the tidal damping likely occurs in the surface regolith layer. As a consequence, Deimos appears to be near its maximum tidal dissipation efficiency (QD ~ 1). An early episode of chaotic tumbling could have initially lowered Deimos' eccentricity to near zero, but this was likely followed by an excitation of its eccentricity through a past resonance with Phobos ca. 2 Gyr ago. This resonance crossing excited Deimos' eccentricity to 0.002, and subsequent synchronous damping over the next 2.5 Gyr requires k2D/QD ~ 7 × 10−5, which still implies efficient damping in Deimos.