Predicted incidence of Jupiter-like planets around white dwarfs

Context. Gas-giant planets and brown dwarfs have been discovered in large numbers around main-sequence stars and even evolved stars. In contrast, and despite ongoing imaging surveys using state-of-the-art facilities, only a handful of substellar companions to white dwarfs are known. It remains unclear whether this paucity reflects observational challenges or the consequences of stellar evolution. Aims. We aim to carry out population synthesis of substellar objects around white dwarfs to predict the fraction and properties of white dwarfs hosting substellar companions. Methods. We generated a representative population of white-dwarf progenitors (up to 4 M⊙) with substellar companions, adopting companion distributions derived from radial-velocity surveys of giant stars and a global age-metallicity relation. We then combined the stellar-evolution codes Modules for Experiments in Stellar Astrophysics (MESA) and Single Star Evolution (SSE) with standard prescriptions for mass loss and stellar tides to predict the resulting population of white dwarfs and their substellar companions. Results. We find that the predicted fraction of white dwarfs hosting substellar companions in the Milky Way is, independent of uncertainties related to initial distributions, stellar tides, or stellar mass loss during the asymptotic giant branch, below ~3 ± 1.5%. The occurrence rate peaks at relatively low-mass (~0.53M⊙ to ~0.66 M⊙) white dwarfs and relatively young (~1-6 Gyr) systems, where it can reach ≳3%. The semimajor axes of the surviving companions range from 3-24 au with a median of 11 au. We estimate that ~95% of the predicted companions are gas-giant planets, which translates to a predicted general Jupiter-like planet occurrence rate around white dwarfs below ~2.9 ± 1.4%. These occurrence rates might slightly increase if multi-planetary systems are considered. Furthermore, owing to the strong dependence of companion occurrence on the metallicity of the white dwarf progenitor, the assumed age-metallicity relation strongly affects the predictions. Based on recent estimates of the local age-metallicity relation, we estimate that the fraction of white dwarfs with companions close to the Sun might reach ≲8%. Conclusions. If the planetary and brown dwarf companion distributions derived from intermediate-mass giant stars through radial velocity surveys reflect the characteristics of the true population, less than 3 ± 1.5% of white dwarfs host substellar companions. Depending somewhat on the age-metallicity relation, this most likely represents an upper limit on possible detections because a significant number of companions might not be detectable with current facilities.