2018MNRAS.474.4603V

The majority of stars both host planetary systems and evolve into a white dwarf (WD). To understand their post-main-sequence planetary system evolution, we present a search for transiting/eclipsing planets and other substellar bodies (SBs) around WDs using a sample of 1148 WDs observed by K2. Using transit injections, we estimate the completeness of our search. We place constraints on the occurrence of planets and SBs around WDs as a function of planet radius and orbital period. For short-period (P < 40 d) small objects, from asteroid-sized to 1.5 R_⊕, these are the strongest constraints known to date. We further constrain the occurrence of hot Jupiters ( < 1.5 per cent), habitable zone Earth-sized planets ( < 28 per cent), and disintegrating short-period planets ( ∼ 12 per cent). We blindly recovered all previously known eclipsing objects, providing confidence in our analysis, and make all light curves publicly available.