The giant nature of WD 1856 b implies that transiting rocky planets are rare around white dwarfs

Abstract

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 atmospheric characterization including biosignatures. Despite this, the first (and still only) transiting planet discovered in 2020 was a roughly Jupiter-sized world, found using 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 rocky planets are highly unusual and the former implying WD 1856 b would have to be highly surprising event at the <0.5% level. Using an HBM, 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 REarth planets are an order-of-magnitude less common than 2-20 REarth planets in the period range of 0.1-10 days. 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.