The very model of a modern Martian moon

Could the two smallest satellites of Mars – Phobos and Deimos – have been formed from a disc of debris blasted into Mars orbit after a giant impact, instead of being captured by Mars as previously assumed? And did a ‘ghost’ moon play a key role in this? Dr Pascal Rosenblatt tells us why numerical models have been key to understanding how these Martian oddities came to be

The origin of the Martian moons remains an open question in spite of numerous space probes sent to the Martian system¹. Two scenarios have been proposed – either Phobos and Deimos are asteroids captured by Mars or they are formed in situ in Mars orbit.

The capture scenario is based on the small size, irregular shape, as well as the low albedo and the cratered surface of the Martian moons, which are very similar to those of asteroids (Figure 1). In the case of Phobos the crater retention age has been estimated at about 4 billion years, meaning it is a very old body – like an asteroid. The main argument supporting the capture scenario comes however from the visible and near-infrared (VIS/NiR) spectra of their surface that are very similar to those of the surface of several asteroids. The point is that Phobos and Deimos could be made of material condensed in the solar nebula at further distance from the Mars' orbit.

[caption id="attachment_55899" align="alignnone" width="620"] Figure 1: Phobos and Deimos (in false colors). Phobos is about 27 km in its longest diameter and Deimos is about 15 km. Images taken by the CRISM instrument onboard Mars Reconnaissance Orbiter. Credit NASA.[/caption]

The spectral data can however be altered by the space weathering processes so that the signature of the moon composition on these spectra could be masked2. Moreover, the spectral data concerns only the surface and could not reveal the bulk composition of both moons – a thin veneer of material coming either from Mars, or from the other moon (Deimos on Phobos surface) or from the inter-planetary space could cover their surface². To work, the capture scenario must explain how the orbit of the asteroid changed just after capture – expected to be in the ecliptic plane and to be very elliptical – into the present near-equatorial and near-circular orbit of both moons. Phobos orbits Mars at 2.7 Mars’ radii and Deimos orbits at 7 Mars’ radii, which is just beyond the synchronous orbit lying at about 6 Mars’ radii (Figure 2). Over the last 30 years, several authors have proposed that a tidal dissipation in Mars and in its moons might accounts for the huge orbital changes required by the capture scenario. However, it is thought impossible to change the orbit of a captured asteroid into the present Deimos orbit over the age of the solar system. It was possible for Phobos – however this requires a tidal dissipation rate inside the moon be closer to that of icy rather than rocky material. Which is unlikely given we know from its bulk density (1.85g/cm3) that while Phobos could contain water ice in its interior, it is not more than one third of its mass¹. Because of the difficulties surrounding a change from the captured orbit into the present orbit of the Martian moons, an alternative scenario of formation in situ has been proposed¹. One such is the giant impact scenario in which a former body hit the proto-Mars (4 to 4.5 billions of years ago) forming a disc of debris – small satellites then formed within this disc³.

[caption id="attachment_55900" align="alignnone" width="620"] Figure 2: The Martian moon system today. Credit Pascal Lee.[/caption]

Numerical simulations – using Smooth Particles Hydrodynamics code – of the formation of a debris disc after a giant collision having formed Borealis Basin in the Northern hemisphere of Mars have shown that a circum-Martian disc can form and extends beyond the orbit of Deimos?. The formation of Phobos and Deimos in a debris disc has also been simulated from a disc confined close to the planet?. In this simulation, the disc is inside the Roche limit (located at 3 Mars' radii) where no moon can be formed because the tidal forces of the planet would pull it apart. But small satellites can form when the disc extends across the Roche limit – as for small moons of Saturn formed from the ring of the planet? – and tens of satellites can then be produced with the size of Phobos and Deimos. But they all orbit well inside the synchronous orbit so that they fall back to Mars in less than 200 million years – which is much faster than the presumed age of Phobos (4 billion years)?. To avoid the problem of tidal receding of the moonlet orbit, one needs to assume that Phobos and Deimos formed in the accretion disc just at each side of the synchronous orbit in order to reach their present orbit by tidal orbital evolution over about 4 billion years?. But the formation of only two small satellites in the outer disc has not been successfully simulated so far?.

Myself and my Belgian, French (Institut de Physique du Globe de Paris) and Japanese (Earth and Life Science Institute, Tokyo Institute of Technology) colleagues have found a solution to this puzzle?. We have shown that a big moon – 1,000 times the mass of Phobos – captures outer-disc material in mean motion resonances, thus facilitating its accretion into two small satellites (Figure 3). To reach this new result, we first re-performed numerical simulations of post-impact disc formation to show that most of the mass of the disc is confined below the Roche limit – forming an inner disc – and that the rest of the material is distributed in a much less dense outer-disc extending beyond the Deimos orbit. The material of the disc is also a mixture of both impactor and target (Mars) material. The evolution of the inner disc was modelled using hydrodynamics representation, allowing for the monitoring of its viscous outward spreading from the planet. In a couple of years the first moons formed at the Roche limit. These moons then migrate outward due to the interaction with the massive inner disc. The most massive moon (1000 times the mass of Phobos or 200 km in diameter) reaches a maximal distance of 4.4 Mars' radii, which is still inside the synchronous limit. After about 5 million years, its orbit recedes back to Mars – because the tidal pull of the planet becomes dominant – accreting all the others moons and destabilising the remaining disc so that big inner moons and the inner disc were removed from the Martian system.

[caption id="attachment_55902" align="alignnone" width="620"] Figure 3. Summary of the giant impact scenario forming Phobos and Deimos. Top: Mars is violently hit by a proto-planet three times as small. The debris form a disc in a few hours. Middle: A large moon rapidly emerges from the disc close to the planet. As it migrates away from Mars, its two zones of (so-called “resonant”) influence propagate like ripples, facilitating accretion of debris further away into two small satellites, Phobos and Deimos, in a few thousand years. Bottom: Due to tides raised by Mars, the large moon falls back to Mars in a few million years, while the smaller Phobos and Deimos reach their present position around Mars within the next billion years. Credit Antony Trinh.[/caption]

In the meantime, the biggest inner moon had a significant effect on the evolution of the outer disc. As the simulation of post-impact disc formation could not resolve for particles as small as Phobos itself, we assumed that the outer disc could be represented as 100 to 1000 satellite-embryos with a mass of less than 1% the mass of Phobos. We then developed a numerical code - using a symplectic integrator – to monitor the gravitational interaction between all these satellite-embryos and the bigger moons formed at the Roche limit, as well as close encounters between them, leading to their accretion. We found that the small embryos are captured in mean motion resonances by the inner big moon. When an embryo is captured by such a resonance, the eccentricity of its orbit increases, making more frequent the close encounters with the others embryos, and their eventual accretion. The efficiency of this mechanism to accrete satellite-embryos is enhanced by the migration of the inner moon, hence the migration of the mean motion resonance location. The effect of the migration of the resonance location is similar to sweeping up the outer disc from its embryo population to end up with two small satellites at each side of the synchronous orbit in a few thousands of years (Figure 3).

We have performed many numerical simulations varying initial conditions for the orbit of satellite embryos, their number and mass distribution in the outer disc as well as the mass of the inner moon. We have found that this mean motion resonance mechanism is robust enough to produce a few satellites at each side of the synchronous orbit. In about 35% of cases, only two satellites are produced with the more massive below and the lighter above the synchronous orbit. In 10% of the cases their masses are even within a few percent of the mass of Phobos and Deimos. The tidal evolution of the orbit of the two outer small satellites has also been computed over 4 billion years. Their orbit can reach the present orbit of Phobos and Deimos assuming tidal dissipation rate in their interior, which are compatible with a rocky composition. This new study shows for the first time that the giant collision scenario can solve the problem of the formation of the moons of Mars thanks to the dynamical effect of a lost massive moon on the outer part of the post-impact circum-Martian disc.

It can even be reconciled with the reflectance spectra of Phobos and Deimos. A recent study? indeed has shown that when considering a gas-to-solid condensation, submicron-sized grains are expected to form. The spectral properties of this fine grained material is similar to those of D-type asteroids and of Phobos and Deimos. In turn, this suggests that the spectra of both Martian moons reflects the conditions prevailing at their formation, like in the outer disc of debris, than the their actual composition. Thus, one does not need anymore to capture material condensed away from Mars to explain the spectra of Phobos and Deimos. An opportunity to check this scenario will soon be available as Phobos sample return missions are in preparation at the Japanese (JAXA) and European (ESA) space agencies – with the possible collaboration of the Russian (Roscosmos) agency – for a likely launch at around 2022 or 2024. Such a returned sample will allow accurate knowledge of the true composition and age of the Phobos. The composition will potentially validate the giant impact scenario depending on whether a Martian mix composition or a pure asteroid composition is found. If the giant impact scenario is compatible with the observed composition, the age will allow us to locate the giant impact event in Mars history. This is of importance for understanding the effect of such a giant impact on the conditions prevailing at Mars surface early in its history.

Dr Pascal Rosenblatt is senior scientist at the Royal Observatory of Belgium (Brussels). He has numerous responsibilities in the scientific exploitation and preparation of space missions to the solar system.

References 1. Pascal Rosenblatt. The origin of the Martian moons revisited. Astronomy and Astrophysics Review 2011. http://dx.doi.org/10.1007/s00159-011-0044-6. 2. Carlé M. Pieters, Scott Murchie, Nicolas Thomas, Daniel Britt. Composition of surface materials on the Moons of Mars, Planetary Space Science 2014. http://dx.doi.org/10.1016/j.pss.2014.02.008. 3. Robert A. Craddock. Are Phobos and Deimos the result of a giant impact? Icarus 2011. http://dx.doi.org/10.1016/j.icarus.2010.10.023. 4. Robert I. Citron, Hidenori Genda, Shigeru Ida. Formation of Phobos and Deimos via a giant impact. Icarus 2015. http://dx.doi.org/10.1016/j.icarus.2015.02.011. 5. Pascal Rosenblatt, Sébastien Charnoz. On the formation of the martian moons from a circum-martian accretion disk. Icarus 2012. http://dx.doi.org/10.1016/j.icarus.2012.09.009. 6. Sébastien Charnoz, Julien Salmon, Aurélien Crida. The recent formation of Saturn’s moonlets from viscous spreading of the main rings. Nature 2010. http://dx.doi.org/10.1038/nature09096. 7. Robin M. Canup, Julien Salmon. On an origin of Phobos-Deimos by giant impact. 47th Lunar and Planetary Science Conference. 2016. 8. Pascal Rosenblatt, Sébastien Charnoz, Kevin M. Dunseath, Mariko Terao-Dunseath, Antony Trinh, Ryuki Hyodo, Hidenori Genda, Stéven Toupin. Accretion of Phobos and Deimos in an extended debris disc stirred by transient moons. Nature Geoscience 2016. http://dx.doi.org/10.1038/NGEO2742.