The origin of Phobos and Deimos is still unknown. They share spectral similarities with outer main belt asteroids, but their planar and quasi circular orbits appear more compatible with formation from a disk (Burns 1992, Rosenblatt 2011). Several properties of Mars seem to require a large oblique collision: its 25-hr day (Dones and Tremaine 1993, Craddock 2011), and the Borealis basin (Marinova et al. 2008, Nimmo et al. 2008). Such impacts would produce a disk with a mass much larger than that of tiny Phobos and Deimos (e.g., Canup & Salmon 2014; Citron et al. 2015). However, most of the mass located inside the synchronous orbit of Mars a_sync ~ 6 Mars radii (R_M) would form large satellites whose orbits would eventually decay due to tidal interactions with the planet. In this scenario, Phobos and Deimos would be the sole two remnants of a once larger population of satellites.
We perform numerical simulations of giant impacts onto Mars, using Smooth Particle Hydrodynamics (e.g., Canup 2004). A series of several tens of simulations, involving an impactor with 3% the mass of Mars (M_M), resulted in disks containing ~10^-4 to 10^-3M_M. A broad range of impact angles and impact velocities produce a Martian day near 25 hr for M_imp = 0.03M_M. Disk material is initially on eccentric orbits, but collisions among the material represented by each SPH particle would rapidly damp eccentricities while approximately conserving angular momentum. Thus debris will relax to a characteristic distance a_eq ≈ a (1-e^2), where a and e are the post-impact semi-major axis and eccentricity of the SPH particle. We estimate the disk’s outer edge by computing the maximum value of a_eq in each simulation. While resulting disks are centrally condensed, they all have 10 to 20% of their mass initially orbiting beyond the Roche limit. Cases producing appropriate length days have outer edges close to Deimos’ orbital radius (~7R_M).
We then investigate the evolution of the disk and accumulation of satellites from disk material using a numerical model developed to study the formation of Earth’s Moon from the protolunar disk (Salmon and Canup 2012). The code represents material within the Roche limit a_R ~ 3R_M as a uniform surface density disk whose mass and outer edge position evolve with time due to viscosity and interactions with outer moons. Material beyond a_R is described by an N-body accretion simulation. We find that in cases with massive disks, very large moons form and accrete all material located initially close to the synchronous orbit. In cases with less massive disks, strong tidal dissipation in Mars can prevent inner moons from expanding outward due to interactions with the Roche-interior disk. When this occurs, analogs to Phobos and Deimos near synchronous orbit may survive.