Modeling the Formation of the Family of the Dwarf Planet Haumea
The dwarf planet (136108) Haumea has an intriguing combination of unique physical properties: near-breakup spin, two regular satellites, and an unexpectedly compact family. While these properties indicate formation by collision, there is no self-consistent and reasonably probable formation hypothesis that can connect the unusually rapid spin and the low relative velocities of Haumea family members ("Haumeans"). We explore and test the proposed formation hypotheses (catastrophic collision, graze-and-merge, and satellite collision). We flexibly parameterize the properties of the collision (e.g., the collision location) and use simple models for the three-dimensional velocity ejection field expected from each model to generate simulated families. These are compared to observed Kuiper Belt Objects using Bayesian parameter inference, including a mixture model that allows for interlopers from the background population. After testing our methodology, we find the best match to the observed Haumeans is an isotropic ejection field with a typical velocity of 150 m s$^{-1}$. The graze-and-merge and satellite collision hypotheses are disfavored. Including these constraints, we discuss the formation hypotheses in detail, including variations, some of which are tested. Some new hypotheses are proposed (a cratering collision and a collision where Haumea's upper layers are "missing") and scrutinized. We do not identify a satisfactory formation hypothesis, but we do propose several avenues of additional investigation. In addition, we identify many new candidate Haumeans and dynamically confirm 7 of them as consistent with the observed family. We confirm that Haumeans have a shallow size distribution and discuss implications for the identification of new Haumeans.