Small particles theoretical scattering simulations for the ESA/HERA mission

The NASA/DART mission demonstrated that a kinetic impact can successfully deflect a dangerous object by altering the orbital period of Dimorphos, the moonlet of the Near Earth, and Potentially Hazardous Asteroid Didymos, by approximately 33 minutes (Daly et al., 2023; Thomas et al., 2023). This significant change was amplified by the recoil of a massive ejecta plume, which transferred more momentum to the asteroid than the spacecraft hit itself (Cheng et al., 2023). As far as the debris are concerned, observations and theoretical simulations showed that while high-velocity particles escaped into heliocentric orbits, slower-moving fragments were subject to the complex gravitational environment of the Didymos system (Li et al., 2023). Over the long term, large boulders and cm-sized particles may remain trapped in the system for years, undergoing chaotic dynamical evolution due to solar radiation pressure and the irregular gravity fields of both asteroids (Rossi et al., 2022; Ferrari et al., 2023). Some of these particles are expected to eventually re-impact the surfaces or stabilize into a temporary, sparse debris disk. Small particles, mm-sized or smaller, have a highly transient survival time within the binary system itself, being heavily influenced by solar radiation pressure and the complex gravitational perturbations from both bodies. Therefore, very small grains in the ejecta cloud either escaped the system rapidly to form the extended dust tail or re-impacted the asteroids within days to weeks (Li et al., 2023; Langner et al., 2024; Langner et al., 2025). Nevertheless, small grains can always be present in the system as the product of ongoing secondary processes such as sesquinary impacts (Langner et al., 2024; Langner et al., 2025), rotational fission and mass shedding (Yu et al., 2019), and interplanetary dust impacts (Yu et al., 2024).

In December 2026 the ESA/Hera mission (Michel et al., 2022) is scheduled to arrive in the asteroidal system to analyse in detail the impact’s long-term effects and characterize the physics of the system itself. One way to infer the intimate nature (composition, shape, and size distribution) of remained small debris or, more generally, small dust particles present in the system, is inverting with theoretical scattering studies remote sensing data as the phase function of possible dust clouds obtained with the Hera/AFC instrument (Vincent et al., 2024). We present a set of theoretical simulations of scattering of sunlight by fractal and irregular particles consisting of asteroidal analogues to define the interpretative framework of future AFC’s phase function data. The simulations were performed with T-matrix and Discrete Dipole Approximation methodologies which allowed us to investigate the scattering behaviour of very small particles. Examples of dispersion properties of spherical larger particles, reaching the cm-sized geometric optics limit, were also performed with modified Mie theory codes.

Bibliographic References

- Cheng, A. F., et al. (2023). "Momentum Transfer from the DART Mission Kinetic Impact on Asteroid Dimorphos". Nature, 616(7957), 457–460.

- Daly, R. T., et al. (2023). "Success ful Deflection of Target Asteroid Dimorphos by DART Kinetic Impact". Nature, 616(7957),443–447.

- Ferrari, F., et al. (2023). "Long-term dynamics around the Didymos–Dimorphos binary asteroid of boulders ejected after the DART impact". Astronomy & Astrophysics, 671, L14.

- Langner et al. (2024). "Long-term dynamics around the Didymos-Dimorphos binary asteroid of boulders ejected after the DART impact". Astronomy & Astrophysics, 684, A151.

- Langner et al. (2025), "Secondary-impact debris in the Didymos system: What could be observed by Hera? ". Astronomy & Astrophysics, Volume 699, A123.

- Li, J.-Y., et al. (2023). "Ejecta from the DART-produced active asteroid Dimorphos". Nature, 616(7957), 452–456.

- Michel, P., et al. (2022). "The Hera mission: European component of the LICIACube and DART planetary defence investigation". The Planetary Science Journal, 3(7), 160. - Rossi, A., et al. (2022). "Dynamical Evolution of Ejecta from the DART Impact on Dimorphos". The Planetary Science Journal, 3(5), 118.

- Thomas, C. A., et al. (2023). "Orbital period change of Dimorphos due to the DART kinetic impact". Nature, 616(7957), 448–451. - Vincent, J.B., et al. (2024). "The Asteroid Framing Cameras on ESA’s Hera mission". EPSC2024-445.

- Yu et al. (2019). "The expansion of debris flow shed from the primary of 65803 Didymos", MNRAS 484,1.

- Yu et al. (2024). Nature Communications 15.

Acknowledgements

We thank the Italian Space Agency (ASI) within the ASI–UniBO agreements 2022-8-HH.0 and 2022-8-HH.1-2025.