On the formation of the martian moons from a circum-martian accretion disk

Abstract

We reconsider two scenarios for the formation of Phobos and Deimos from a circum-martian accretion disk of debris: the strong tide regime for which accretion occurs close to the planet at the Roche limit and the weak tide regime for which accretion occurs farther from the planet. We assume a disk with an initial mass of 1018kg (Craddock, R.A. [2011]. Icarus 211, 1150–1161). In the strong tide regime, the disk loses its material by viscous spreading inward to and outward from the planet. When outward moving material crosses the Roche limit, small-sized moonlets are accreted from gravitational instabilities with a shape and density similar to Phobos and Deimos. Due to the gravitational torque exerted by the disk, the moonlets migrate away from the planet, though they cannot reach the synchronous orbit (lying at 6 Mars’ radii). After the disk has lost most of its mass they rapidly fall back onto Mars due to the tidal decay of their orbits. Although, the total mass of moonlets is comparable to the mass of Phobos, their survival time does not exceed 200Ma, which is incompatible with the formation of Phobos and Deimos early in Mars’ history. In the weak tide regime, moonlets can accrete near the synchronous orbit with the mass of Deimos in a disk of up to 1018kg (similarly to planetary embryos formation in the protoplanetary disk). A Phobos-mass embryo can also be formed in the same disk but closer to Mars (at 3–4 Mars’ radii) so that it rapidly falls back onto Mars by tidal decay of its orbit. However, several embryos may accrete together in the disk (similarly to the final stage of terrestrial planet formation), and Phobos and Deimos may be the last two remnants of those bodies formed near the synchronous distance to Mars. Further investigations are still needed to understand such accretion mechanism within a circum-martian disk primarily extending below the synchronous orbit.