Predicted incidence of Jupiter-like planets around white dwarfs

Only a handful of gas giant planets orbiting white dwarfs are known. It remains unclear whether this paucity reflects observational challenges or the consequences of stellar evolution. 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. We generated a representative population of white-dwarf progenitors with substellar companion and used the stellar-evolution codes MESA and SSE with standard prescriptions for mass loss and stellar tides to predict the resulting population of white dwarfs and their companions. 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%. The occurrence rate peaks at relatively low-mass (~0.53 Msun to ~0.66 Msun) white dwarfs and relatively young (~1-6 Gyr) systems, where it exceeds 3%. The semimajor axes of the surviving companions range from 3-24 au. We estimate that ~95% of the predicted companions are gas-giant planets. 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%. 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% of white dwarfs host substellar companions. This most likely represents an upper limit on possible detections because a significant number of companions might not be detectable with current facilities.