Asteroid mass estimation with the robust adaptive Metropolis algorithm

Abstract

The bulk density of an asteroid informs us about its interior structure and composition. To constrain the bulk density one needs an estimate for the mass of the asteroid. The mass is estimated by analyzing an asteroid's gravitational interaction with another object, such as another asteroid during a close encounter. An estimate for the mass has typically been obtained with linearized least-squares methods despite the fact that this family of methods is not able to properly describe non-Gaussian parameter distributions. In addition, the uncertainties reported for asteroid masses in the literature are sometimes inconsistent with each other and suspected to be unrealistically low. We present a Markov-chain Monte Carlo (MCMC) algorithm for the asteroid mass estimation problem based on asteroid-asteroid close encounters. We verify that our algorithm works correctly by applying it to synthetic data sets. We then use astrometry available through the Minor Planet Center to estimate masses for a few example cases and compare our results to results reported in the literature. Our mass estimates for the synthetic data sets are fully consistent with the ground truth. The nominal masses for real example cases typically agree with the literature but tend to have greater uncertainties than what is reported in recent literature. Possible reasons for this include different astrometric datasets and/or weights, different test asteroids, different force models and different algorithms. For (16) Psyche, the target of NASA's Psyche mission, our maximum likelihood mass is approximately 55% of what is reported in the literature. Such a low mass would imply that the bulk density is significantly lower than previously expected and hence disagrees with the theory of (16) Psyche being the metallic core of a protoplanet. We however note that masses reported in recent literature remain within our 3-sigma limits.