On the forced planes of the Hilda asteroids and other resonant groups

Laplace-Lagrange linear secular theory describes the mean orbit plane forced by the massive planets for small body populations outside mean motion resonances. The mean planes of several non-resonant populations inside the asteroid belt and Kuiper belt have been shown to match the Laplace plane to within the statistical limits imposed by the observed populations and the methods used in calculating the mean plane. Although linear secular theory is considered inapplicable within mean motion resonances, we show that it describes the forced planes of the Hilda asteroids in Jupiter’s interior 3:2 mean motion resonance and of the Hilda and Schubart collisional families therein, to the level of statistical precision with which those can be computed from the orbital data. We use the Hilda asteroids as a test population because they are observationally complete up to absolute magnitude H ≈ 15.7, and up-to-date catalogs are available to identify collisional families therein. This gives a statistically useful sample of thousands (n ~ 2100) of resonant objects that can be studied on a population level while limiting the statistical uncertainties to those inherent in parameter estimation without the need to account for the observational biases of various sky surveys. At the present time and for at least 2 Myr into the future, the mean orbit planes of the Hilda collisional family and the Schubart collisional family are statistically indistinguishable from each other and from the local instantaneous Laplace plane as predicted by Laplace-Lagrange linear secular theory based on the known planets. However, they are also statistically indistinguishable from the orbit plane of Jupiter. We estimate that a sample population ~100 times larger is necessary to statistically distinguish between the Laplace plane and Jupiter plane as hypothetical “true” forced planes for the Hilda asteroids. In the coming decade, the Rubin observatory may be able to push the completeness limit to dimmer magnitudes and enable a more sensitive test of Laplace theory within the Hilda region. For more tests of Laplace theory for resonant populations, we consider the mean plane of the Hilda asteroids in a solar system with a fictitious more massive, highly inclined Saturn, and we study the mean planes of the Plutino and Twotino groups in the Kuiper belt. As of the time we write this abstract, we do not have results for these last-mentioned studies, but we hope to have preliminary findings to share by the time of the conference. IM gratefully acknowledges funding by NASA FINESST grant #80NSSC23K1362.