Predicted incidence of Jupiter-like planets around white dwarfs

TL;DR

This work tackles the incidence and properties of Jupiter-like planets around white dwarfs by performing a population synthesis that starts from WD progenitors with substellar companions drawn from RV surveys and an age-metallicity relation. Using SSE for rapid stellar evolution and MESA for detailed late-AGB evolution, combined with the FATES orbit-evolution module, the study quantifies how mass loss and tides sculpt the survival of companions. The main result is that the fraction of WDs hosting substellar companions is below ~3% (with ~95% of those companions being gas giants), and that the surviving planets typically reside at 3–24 AU, with a median near 11 AU; this fraction is highly sensitive to metallicity and the tidal prescription. The findings imply that detectable WD companions are intrinsically rare, though local population variations in metallicity could raise the nearby incidence to as high as ~8%, and observational opportunities with next-generation facilities may still uncover a subset of these systems.

Abstract

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.

Figures (6)

• Figure 1: Orbital evolution of a $1$ M$_{\mathrm{J}}$ gas-giant planet orbiting a $2$ M$_{\odot}$ star with $Z=0.0187$, comparing calculations performed with SSE (left), the MESA default test suite (middle), for which the AGB mass-loss efficiency is set to $\eta=0.7$, and MESA assuming a more realistic mass-loss efficiency ($\eta= 0.02$; right). The orbits are assumed to be circular, and initial separations range from $2$ to $4.5$ au, with a step size of $0.5$ au. The red filled area corresponds to the stellar radius, while purple and green lines denote the orbital separation of the engulfed and surviving planets, respectively. The insets show zoomed-in views of the thermal pulse phase of the AGB and highlight its critical role in planetary engulfment. SSE does not account for the thermal pulses (left). For a large mass-loss efficiency (middle), most planets survive because the orbit expansion caused by stellar mass loss dominates. In the most realistic scenario assuming a small efficiency (right), the star evolves through more thermal pulses and reaches a larger radius, which causes most planets to be engulfed.
• Figure 2: Survival of a $10$ M$_{\mathrm{J}}$ gas-giant planet orbiting a $2$ M$_{\odot}$ star for different initial semimajor axes and eccentricities. Red stars indicate engulfment, while blue circles stand for survival of the planet. We assumed two different approximations for the convective turnover time, $\tau_{\mathrm{conv}}$. Following [][]rasioetal96-1 (right panel), many more planets are engulfed than when assuming the prescription suggested by [][]Villaver_2009 (left panel). In both cases, the survival of substellar objects depends on the eccentricity of the orbit, with more eccentric orbits leading more frequently to engulfment. Due to stronger tides, this dependence is more pronounced assuming the approximation by [][]rasioetal96-1. For initial semimajor axes $\geq8$ au, the effects of tidal forces are negligible except for very large eccentricities.
• Figure 3: Survival of substellar companions as function of companion mass (top), initial semimajor axis (middle), and initial eccentricity (bottom). The left panels represent results when considering the tidal force model by Villaver_2009, while the right panels show results when using the tidal force model by rasioetal96-1. All distributions are normalized by the total number of stars (1000). The number of surviving companions is indicated in the figure for each model (blue histogram). The vertical lines correspond to the median value of each sample. The solid lines correspond to the cumulative distributions. In general, the initial distributions of surviving companions (orange) are shifted toward lower masses, larger semimajor axes, and smaller eccentricities compared to the initial values of all companions (blue). These effects are slightly more pronounced for stronger tides (right panels).
• Figure 4: Final and initial properties of systems that host a susbtellar companion. Each row shows a set of histograms comparing two WD samples: one modeled using [][]Villaver_2009 (left) and one based on the [][]rasioetal96-1 (right) approximation for stellar tides. All histograms are normalized to the total number of surviving companions for each simulation. The final semimajor axes are significantly larger than the initial ones for both tidal prescriptions (top left). For weak tides, the eccentricity distribution does not significantly change, while the distribution moves slightly toward smaller eccentricities for strong tides (top right). The bottom panels show the WD mass and age distributions for both approximations of tidal forces which appear to be rather similar.
• Figure 5: Fractions of WDs hosting substellar companions as function of total system age and WD Mass. The total fraction of WDs with substellar companions is $1.3$ % [assuming weak tides][top left]Villaver_2009 and $0.6$ % for stronger tides according to rasioetal96-1. In both cases, companions are more likely around lower mass WDs and relatively young systems. In particular, for higher mass stars, stronger tides lead the radius expansion to dominate over orbital expansion, and therefore only planets around lower mass stars survive. The extension of the region with high probabilities is therefore very sensitive to the strengths of the tides. For example, further increasing the tides according to rasioetal96-1 by a factor of $8/3$ would eliminate the remaining small high probability island in the right panel.