Tidal disruptions of rubble piles: The case of Phobos

Abstract

Many small satellites in the Solar System have sub-synchronous orbits, meaning their orbits are decaying due to tidal dissipation. Unless they have substantial material strength, they will eventually tidally disrupt before reaching their planet's surface. We studied the fate of rubble-pile satellites as they migrate inward, with a particular focus on the case of Phobos. We used a combination of analytic estimates and numerical simulations to determine the failure mode and tidal disruption distance of a Phobos-like satellite, as a function of its shape and cohesive strength. Both analytically and numerically, we identify a regime for satellites with low cohesive strengths whereby their surface can be tidally stripped without undergoing internal failure. Our numerical simulations demonstrate that Phobos will be destroyed beyond 2 Mars radii if it has a bulk strength similar to those estimated for small bodies recently visited by spacecraft. Based on our results and some additional arguments, we suggest that previous studies on the fate of Phobos have overestimated its strength, and therefore underestimated its tidal disruption distance. We also speculate that if Phobos undergoes some tidal stripping, its ultimate fate may be determined by runaway collisional erosion rather than a pure tidal disruption. However, the ultimate tidal disruption distance for Phobos will depend on its unknown internal structure and bulk material properties, which will be constrained by JAXA's Martian Moons eXploration (MMX) mission and its IDEFIX rover. These results have implications for theories about the origin and evolution of the Martian moons and for tidal disruptions of other small, irregularly shaped satellites.

Figures (7)

• Figure 1: Second-order rigid-body Roche limit, referred to as $d_\text{strip}$, for a uniform-density triaxial ellipsoid around Mars, as a function of its axis ratios $a/b$ and $b/c$. With Phobos' present-day bulk density and shape, the surface acceleration at the sub-Mars point will become zero at ${\sim}2.03R_\text{M}$, meaning that material could be freely stripped from the surface.
• Figure 2: Difference between the predicted distance for tidal stripping ($d_\text{strip}$) and the distance for disruption ($d_\text{disrupt}$), measured in Mars radii, as a function of a satellites axis ratios. When this difference is positive, tidal stripping is predicted to occur before internal failure (and tidal disruption). The satellite is assumed to have a triaxial shape, uniform density, a friction angle of $35^\circ$, and zero cohesion.
• Figure 3: Renderings of the rubble-pile models of Phobos used for this study. The top row shows a top-down rendering, looking down from Phobos' spin pole with Mars oriented to the left. The bottom row shows an edge-on view, where the camera is trailing Phobos orbit and Mars is to the left.
• Figure 4: Time-series plots showing the semimajor axis ($a_\text{orb})$, the amount of lost mass ($M_\text{lost}/M_\text{P}$), and the change in the average contact number ($\Delta\bar{N}_c$) for the three rubble pile models of Phobos for different bulk cohesive strengths. The ellipsoidal case is shown in panel (a), while the low- and high-resolution cases with the real Phobos shape are combined in panel (b).
• Figure 5: Snapshots of the cohesionless, high-resolution Phobos case, in a coorbiting frame looking down from Phobos spin pole with Mars oriented to the left. Each frame indicates the simulation time, orbital distance, and orbital period (which equals Phobos spin period). The particle colors indicate their net acceleration magnitude relative to Phobos' center of mass. Several mass shedding events occur starting at ${\sim}2.25R_\text{M}$ until Phobos is finally disrupted at ${\sim}2.09R_\text{M}$. There are many mass shedding events in addition to the three shown in this figure and we refer the reader to the animated version of this figure.