2024MNRAS.527.3532K

White dwarfs (WDs) have roughly Earth-sized radii - a fact long recognized to facilitate the potential discovery of sub-Earth-sized planets via transits, as well as atmospheric characterization including biosignatures. Despite this, the first (and still only) transiting planet discovered in 2020 was a roughly Jupiter-sized world, found using Transiting Exoplanet Survey Satellite (TESS) photometry. Given the relative paucity of giant planets compared to terrestrials indicated by both exoplanet demographics and theoretical simulations (a 'bottom-heavy' radius distribution), this is perhaps somewhat surprising. Here, we quantify the surprisingness of this fact accounting for geometric bias and detection bias assuming (1) a bottom-heavy Kepler-derived radius distribution and (2) a top-heavy radial velocity-inspired radius distribution. Both are concerning, with the latter implying that rocky planets are highly unusual and the former implying that WD 1856 b would have to be highly surprising event at the <0.5 per cent level. Using a hierarchical Bayesian model, we infer the implied power-law radius distribution conditioned upon WD 1856 b and arrive at a top-heavy distribution, such that 0.1-2 R_⊕ planets are an order-of-magnitude less common than 2-20 R_⊕ planets in the period range of 0.1-10 d. The implied hypothesis is that transiting WD rocky planets are rare. We discuss ways to reconcile this with other evidence for minor bodies around WDs, and ultimately argue that it should be easily testable.