Challenges in forming Phobos and Deimos directly from a splitting of an ancestral single moon

The origin and evolution of Martian moons have been intensively debated in recent years. It is proposed that Phobos and Deimos may originate directly from a splitting of an ancestral moon orbiting at around the Martian synchronous orbit. At this hypothetical splitting, the apocenter of the inner moon (presumed as Phobos) and the pericenter of the outer moon (presumed as Deimos) are reported to coincide, in that, their semi-major axes reside inside and outside the Martian synchronous orbit with non-zero eccentricities, respectively. However, the successive orbital evolution of the two moons is not studied. Here, we perform direct $N$-body orbital integrations of the moons, including the Martian oblateness of the $J_2$ and $J_4$ terms. We show that the two moons, while they precess, likely collide within $\sim 10^4$ years with an impact velocity of $v_{\rm imp} \sim 100-300$ m s$^{-1}$ ($\sim 10-30$ times moons' escape velocity) and with an isotropic impact direction. The impact occurs around the apocenter and the pericenter of the inner and outer moons, respectively, where the timescale of this periodic orbital alignment is regulated by the precession. By performing additional impact simulations, we show that such a high-velocity impact likely results in a disruptive outcome, forming a debris ring at around the Martian synchronous orbit, from which several small moons would accrete. Such an evolutionary path would eventually form a different Martian moons system from the one we see today. Therefore, it seems unlikely that Phobos and Deimos are split directly from a single ancestral moon.