A comparative study of size frequency distributions of Jupiter Trojans, Hildas and main belt asteroids: A clue to planet migration history

Abstract Since 2002, we have obtained size frequency distributions (SFDs) of main belt asteroids (MBAs), Hildas, and Jupiter Trojans (JTs) by using the 8.2-m Subaru Telescope equipped with the wide-field CCD cameras: Suprime-Cam (SC) or Hyper Suprime-Cam (HSC). After combining these SFDs with SFDs obtained from other surveys, we performed a comparative study of SFDs for each group of small bodies in an attempt to obtain clues about planet migration that affected those populations. The large aperture of the Subaru Telescope and the wide field of view of SC or HSC allowed us to detect small moving objects up to apparent magnitudes 24.4–24.5 mag ( R c -band), which corresponds to sub–km in diameter ( D ) for MBAs and about 1 km for Hildas and JTs. We combined the SFDs obtained from our surveys with those derived from published data to obtain the individual representative SFD for MBAs, Hildas and JTs in the size range of sub–km to 1000 km. We found that the SFDs of JTs and Hildas are roughly flat in the R -plot while that of MBAs has a wavy structure. We also investigated the SFDs of MBAs in the inner, middle, and outer regions of the main belt. We found that the shape of the SFDs changes gradually with increasing heliocentric distance across these regions. This trend continues beyond the outer region, where the SFD becomes flatter as shown by the SFDs of JTs and Hildas. Recent planet migration models suggest that the current JTs originated in the trans-Neptunian region and were captured as Trojans during planet migration. The finding of a gradual change of the SFDs from the inner MBAs to JTs is in line with the idea that trans-Neptunian objects (TNOs) were implanted not only into the JT region, but also into the main belt outer region (including the Hildas) at the early solar system. In order to investigate this implantation hypothesis, we considered a synthetic population of TNOs assuming with a SFD represented by a power-law distribution of N > D ∝ D - 3 , (estimated from crater record on Pluto and Charon). We then added this synthetic population to the MBA populations in various proportions. We found that the higher the proportion, the flatter the wavy SFD of MBAs becomes. This simple model yields a rough explanation for the gradual change of SFDs found from the inner main belt to the JT region. However, the shape of the modelled SFDs does not match observations for all sizes. In particular, because important discrepancies are seen in the small size range, we need to consider the removal of small objects by collisional evolution and/or Yarkovsky effect in the future.