Collisional study of Hilda and quasi-Hilda asteroids

Abstract: The Hilda asteroids are located in the outer main belt in a stable 3:2 mean-motion resonance with Jupiter, while the quasi-Hildas (qH) have similar orbits but are not directly under the effect of the MMR. Moreover, cometary activity has been detected in qH. In this study, we investigate the collisional evolution of Hilda asteroids and apply it to study the cratering on asteroid 334 Chicago, as well as to determine whether impacts between Hildas and qH can serve as a viable mechanism for inducing cometary activity. We simulated the collisional evolution of Hilda asteroids over a period of 4 Gyr. We considered three initial size-frequency distributions (SFD) and two scaling laws for the collisional outcomes and performed a large set of simulations for each scenario which we used to construct median SFDs of the Hilda population. We also derived impactor SFD on asteroid 334 Chicago and used it to calculate the crater SFD on 334 Chicago. Additionally, we evaluated the subcatastrophic impact timescale between Hilda and qH objects. The observed SFD of Hilda asteroids larger than 3 km is best matched by scenarios assuming that such SFD is mostly primordial, implying minimal collisional activity over time. For smaller sizes, although unconstrained, the SFD steepens significantly due to the catastrophic fragmentation of a small number of multikilometer-sized bodies. We determined that the largest impactor on 334 Chicago measures a few kilometers in size, resulting in a maximum crater size of approximately 30 km. Furthermore, the slope of the crater SFD mirrors that of the initial SFD for subkilometric bodies. While impact events between Hildas and qH can induce observable activity and although stochastic in nature, the timescale of such events exceeds the dynamical lifetime of qH, making them an unlikely primary mechanism for inducing observable activity.