Gravitational scattering of ejecta in the Didymos system cannot explain the evolution of the binary's orbital period

Context. In the first few months following the DART impact on Dimorphos, it appears that the orbital period dropped by ∼30 s in addition to the immediate ∼30 min drop. This effect has been attributed to “binary hardening”, whereby the binary's orbital period would have gradually decreased as Dimorphos continuously scattered bound ejecta out of the system and lost angular momentum. Aims. We investigated this hypothesis with the goal of constraining the conditions that would lead to a gradual decrease in the binary's orbital period. Methods. We used N-body simulations to study the dynamical evolution of the Didymos system under the influence of a cloud of massive test particles. Results. We demonstrate that the gravitational scattering of ejecta is not a plausible explanation for Dimorphos's anomalous orbital period drop under any circumstances. This is a result of Dimorphos's escape speed being low compared to its orbital velocity, making it a weak scatterer. Conclusions. If a significant fraction of DART ejecta was launched at low speeds, as impact models and scaling laws suggest, then the binary's orbital period was likely increased as this material was accreted back onto Didymos and Dimorphos. Therefore, some additional mechanism must have overcome this effect, leading to a net orbital period decrease.