The Sesquinary Catastrophe on Deimos can reconcile its excited past with its dynamically cool present

TL;DR

This work addresses how Deimos could have originated with orbital excitation yet retain its present low-eccentricity and modest inclination. It introduces the sesquinary catastrophe, a runaway cascade of high-velocity ejecta re-impacting a moon, creating a debris disk that circularizes and re-accretes into a dynamically cooler body. Through N-body simulations with collisional fragmentation (FRAGGLE) and semi-analytical modeling, the authors show that if Deimos carried substantial excitation, it would undergo rapid erosion and breakup on timescales of about $10^{3}$–$10^{4}$ years, with a threshold near $q \approx 8$ governing the onset. The resulting re-accretion would yield a porous, rubble-pile moon with a smooth surface, offering a self-consistent pathway to reconcile past dynamical states with current observations and potentially applying to other moons such as Adrastea and Thebe, pending observational validation from missions like MMX.

Abstract

The origins of the Martian moons Phobos and Deimos are highly debated, and hypotheses include formation from an impact-generated circum-Martian disk or from capture of asteroids. With the impact scenario, Deimos (or its precursors) were formed or were pushed out beyond the synchronous orbit of Mars. Moons interior to the synchronous orbit, including Phobos (or its precursors), would tidally evolve and resonances between these moons could potentially excite Deimos' orbit. This contradicts Deimos' present-day orbit of low eccentricity ($0.00027$) and moderate inclination ($1.8^\circ$ to the Laplace plane). Tidal dissipation within Deimos is too inefficient for eccentricity damping, and without alternative mechanisms, Deimos' present-day orbit places strong constraints on the evolution of any inner moons. We propose that a runaway collisional cascade called the "sesquinary catastrophe'' acts as a natural barrier that prevents Deimos from having a more excited orbit. Using N-body simulations with collisional fragmentation, we show that if Deimos was more excited, it would undergo a sesquinary catastrophe and break apart into a Roche-exterior debris disk. Using a measure of sesquinary orbital excitation called $q$, our simulations and previous works suggest that breakup occurs for $q \gtrsim 8$ on timescales of $\sim 10^{3-4}$ years. If Deimos was destroyed in a sesquinary catastrophe and re-accreted from a (likely collisionally) damped debris disk, it should be a porous sand-pile moon, consistent with its smooth surface. The sesquinary catastrophe can be applied to other Deimos-like planetary moons at $q \gtrsim 8$.

Figures (6)

• Figure 1: Typical sesquinary catastrophe behavior in a Mars-centric frame. Panel (a) shows the initial simulation setup described in section \ref{['sec:sim set up']}. Deimos (and therefore the ejecta) is given an excitation $q = 0 - 40$ by giving it a higher $e$ and/or $i$. Ejecta from Deimos has an initial velocity $v = 1-3 \ v_{escape}$ with total ejecta mass $M_{impactor} = 10^{-3} \ M_{Deimos}$ unless mentioned otherwise. The gravitational harmonics for Mars from GMM3 Genova2016SeasonalScience are also included up to degree and order 6. Repeated sesquinary impacts quickly fill up the region of Deimos and create an ejecta debris ring. The high-velocity re-impacting ejecta contribute to this runaway sesquinary erosion. Phobos, Deimos, and impactor particles are scaled up for visual ease.
• Figure 2: Mass evolution of Deimos in the sesquinary catastrophe vs time for various initial excitations via N-body simulations. This shows large-scale mass loss due to the sesquinary catastrophe across a range of excitations $q$, proportional to the excitation level. In the early stages, we see some accretion because not all particles have precessed enough out of alignment to gain erosive impact velocities. We show selected simulations for visual ease, but about $90$ simulations were run that show similar behavior.
• Figure 3: Mass evolution of Deimos at initial $e = 0.05$ and $i = 5^\circ$ in the sesquinary catastrophe vs time at different initial mass steps via accelerated N-body simulations. The mass lost from Deimos is put into large impactors so that total mass of the system is the same. This accelerates the simulations with more mass loss per impact, and qualitatively show that complete breakup is possible. NOTE: "sim units" in each simulation are based on years. We present the time in "sim units" rather than years to emphasize that each simulation has a different time scaling because of the inflated impact rate, and the remnant mass is not a continuous function of time.
• Figure 4: Probability density function (PDF) fits to the normalized $v_{impact}$ data. We combine and normalize the impactor velocity ($v_{impact}$) data across all simulations and fit the distribution to multiple PDFs using SciPy Virtanen2020SciPyPython. Here is the best fit log-normal distribution with the fitting parameters in the legend.
• Figure 5: Semi-analytical mass vs time for Deimos as a function of initial $q$. Given an initial excitation $q$, we can calculate the mass evolution over time. There is a slow erosion of the excited Deimos until it reaches the "tipping point" of $0.99 - 0.95 \ M_{Deimos}$, after which the erosion is very quick because of the increased flux of impactors. Of the total time for break-up, $\sim 50 \%$ of it is spent reaching $0.99 \ M_{Deimos}$ and then next $\sim 50 \%$ is spent reaching the final value of $0.01 \ M_{Deimos}$.