Orbital and absolute magnitude distribution of Hilda population

The Hilda population of asteroids is located in a large orbital zone of long-term stability associated with the Jupiter J3/2 mean motion resonance. They are a sister population of the Jupiter Trojans, since both of them are likely made up of objects captured from the primordial Kuiper belt early in the solar system history. Comparisons between the orbital and physical properties of the Hilda and Trojan populations thus represent a test of outer planet formation models. Here we use a decade of observations from the Catalina Sky Survey (G96 site) to determine the bias-corrected orbital and magnitude distributions of Hildas. We also identify collisional families and the background population by computing a new catalog of synthetic proper elements for Hildas. We model the cumulative magnitude distribution of the background population using a local power-law representation with slope $\gamma(H)$, where $H$ is the absolute magnitude. For the largest Hildas, we find $\gamma\simeq 0.5$ with large uncertainty due to the limited population. Beyond $H\simeq 11$, we find that $\gamma$ transitions to a mean value ${\bar \gamma}=0.32\pm 0.04$ with a slight dependence on $H$ (significantly smaller than Jupiter Trojans with ${\bar \gamma}=0.43\pm 0.02$). We find that members of identified collisional families represent more than $60$\% of the total population (both bias counts). The bias-corrected populations contain about the same number of Hildas within the families and the background for $H\leq 16$, but this number may increase to $60$\% families when their location in the orbital space is further improved in the future.