Long term dynamics of boulders in the Didymos-Dimorphos binary asteroid system

On September 26, 2022 the DART probe impacted Dimorphos, the small moon of the binary 65803 Didymos asteroid system.
The event generated a large ejecta plume that was imaged first by the small LICIACube cubesat, released by DART 15 days before the impact, during its
fly-by. The images revealed a complex plume with a cone-like structure, crammed with dust, clumps of objects, filaments and larger boulders.  The event and the resulting ejecta were also observed by several space and ground based observatories which allowed the characterization of the plume evolution and, in
particular, the formation of a long tail of debris, pushed by the solar radiation pressure, stretching for thousands of km. Further observations by the
Hubble Space Telescope revealed the presence of a large population of dozens of boulders moving in the surroundings of the system. Assuming a geometric albedo of 0.15, these large objects span a range of dimensions between about 4 to  ∼ 7 m in diameter. Jewitt and co- authors estimated sky-plane velocities in the range between 10 cm/s to more than 67 cm/s, without significant correlation between the size and the velocity of the boulders. Since the escape velocity
from the binary system is about 24 cm/s, these velocities are consistent with objects that do not re- impact Dimorphos right after the ejection and that can
stay within the system for a comparatively long time span on highly perturbed chaotic orbits.
The long term dynamical behavior of a synthetic population of ejected boulders is investigated for a timespan of about 4 years (corresponding to the arrival of Hera at the system) by means of a comprehnsive model including the relevant perturbations, namely, the gravitational forces from both asteroids (using quadrupole potential), the gravity of the Sun and the Solar radiation pressure. The ephemeris for Sun, Didymos and Dimorphos are implemented using the NASA Spice Kernels.

During their evolution, the fragments may have frequent close encounters with either components of the binary asteroid, making their orbits highly chaotic.
The most probable outcomes of the boulders evolution is either ejection from the system or re-impact against one of the asteroids.
About 1  % of the simulated population survived for the whole integration time span.
The long surviving objects follow a complex dynamical evolution which often includes the increase in the orbital inclination and orbital flips which are similar to the Kozai mechanism. For many of these orbits we observe the increase of orbital inclination resulting in the object entering close to polar orbits or orbital flips from retrograde to prograde or vice-versa. Quasi-satellite orbits, weakly bounded to the binary system are reached too (see  Fig. 1).

Figure 1: Examples of the orbits of long lasting boulders.

The distribution of the re-impact locations on the surfaces of the asteroids is not uniform (see Fig. 2).

Figure 2: Location of re–impacts on Didymos (left) and on Dimorphos  (right). In the right panel, the green dot marks the DART impact location and the (0°,0°) point is the direction towards Didymos and the North pole (+ 90° latitude) is in the direction of the rotation axis, while the other one (-90°,0°) is the direction of the Dimorphos orbital motion. Most of the re-impacts are concentrated near the point (90°,0°) that is opposite the direction of orbital motion of Dimorphos and almost opposite the DART impact location.

The maps of the re-impacting locations are computed. The outcomes of the low velocity re-impacts (at about 50 cm/s) are evaluated through dedicated iSale hydrocode (see Fig. 3) simulations providing support for the analysis of the forthcoming Hera images.

Figure 3: Snapshots at 19.50 s of a 10 \% basaltic projectile of 1 m in diameter, impacting on a 60 \% target. The upper and lower plots show the simulations with the Drucker-Prager (DRPR) and Lundborg (LUND) strength models, respectively. The right panels show the case of a 45 cm/s impact, whereas the left panels show that of a 65 cm/s impact. A slightly different ejection angle of the ejecta curtains can be observed between the two models. The colours refer to the different materials of the projectile (blue) and target (yellow), which have different porosity.