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Predicted incidence of Jupiter-like planets around white dwarfs

Through population synthesis modeling, the study predicts that fewer than 3% of white dwarfs in the Milky Way host surviving substellar companions (mostly gas giants), a fraction that could reach approximately 8% near the Sun depending on metallicity, though current detection rates may remain lower due to observational limitations.

Original authors: Alex Mauch-Soriano, Matthias R. Schreiber, Diego Correa, Julio Pinilla, Catalina Riveros-Jara, Javiera Vivanco, Maria Paula Ronco, Diogo Belloni, Felipe Lagos-Vilches, Wolfgang Brandner

Published 2026-01-28

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CC BY 4.0

Original authors: Alex Mauch-Soriano, Matthias R. Schreiber, Diego Correa, Julio Pinilla, Catalina Riveros-Jara, Javiera Vivanco, Maria Paula Ronco, Diogo Belloni, Felipe Lagos-Vilches, Wolfgang Brandner

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Milky Way as a giant, bustling city. For years, astronomers have been counting the "apartments" (planets) in the buildings (stars) of this city. They know that almost every main-sequence star (like our Sun) has at least one planet. Since stars eventually die and shrink down into tiny, dense "ghosts" called white dwarfs, it seems logical to assume that these ghost stars should still have their planets hanging around.

However, when astronomers look at these white dwarfs with their most powerful telescopes, they are finding almost no planets. It's like walking through a neighborhood of old, retired houses and finding them all empty, even though the owners used to have families.

This paper asks: Are the planets actually gone, or are we just bad at finding them?

To answer this, the authors didn't just look through a telescope; they built a massive cosmic simulation—a digital time machine. Here is how they did it and what they found, explained simply:

1. Building the Digital City

The researchers created a virtual population of over 240,000 stars. They didn't just pick random stars; they used real data from surveys of giant stars (the "middle-aged" versions of stars) to decide how many planets each star started with.

The Analogy: Imagine they took a census of all the families in a city today, figured out how many kids each family had, and then used that data to predict how many kids those families would have had 10 years ago.

2. The Great Cosmic Shrinking

Stars don't stay the same size forever. As they age, they puff up into giant red balls (Red Giants) and then shrink down to white dwarfs.

The Danger Zone: When a star puffs up, it's like a balloon inflating inside a room. Any planet too close (within about 1 "astronomical unit," or the distance from Earth to the Sun) gets swallowed whole.
The Escape: Planets that are far away usually survive. As the star loses weight (mass) during its giant phase, the planets' orbits expand, pushing them further away, like a skater spinning faster when they pull their arms in, but in reverse.

3. The "Tides" and "Wind" Factors

The simulation had to account for two invisible forces that determine if a planet survives:

Stellar Wind (Mass Loss): As the star sheds its outer layers, it pushes the planets outward.
Stellar Tides: Think of this like the moon pulling on Earth's oceans. A giant star can pull on a nearby planet, dragging it closer and potentially swallowing it. The authors tested two different theories on how strong these "tides" are: a "weak tide" model and a "strong tide" model.

4. The Results: The Planets are Rare

After running the simulation through billions of years of virtual time, the results were surprising but clear:

The Big Number: Even in the best-case scenario (where tides are weak and planets are lucky), less than 3% of white dwarfs are expected to have a surviving planet.
The "Jupiter" Connection: Of the few planets that do survive, about 95% are "Jupiter-like" gas giants. Small, rocky Earth-like planets are likely too small to survive the journey or were never there in the first place.
Where are they? The surviving planets aren't hugging the white dwarf; they are far away, orbiting at distances between 3 and 24 times the Earth-Sun distance.

5. Why the Numbers Vary (The "Metal" Factor)

The authors found that the answer depends heavily on the "metallicity" of the star (how many heavy elements it has).

The Analogy: Think of metallicity as the "quality of ingredients" in a recipe. Stars with more "ingredients" (metals) are more likely to have planets.
The Twist: The simulation used a global recipe for the whole galaxy. However, if you look at the specific neighborhood around our Sun, the "recipe" might be different, potentially raising the number of planets to about 8%. But even then, it's still a small fraction.

6. The Conclusion: It's Not Just Bad Telescopes

The paper concludes that the reason we haven't found many planets around white dwarfs isn't just because our telescopes aren't good enough. The planets are likely just not there.

The vast majority of planets around dying stars probably get swallowed up or ejected into space during the star's dramatic transformation. The few that remain are rare, distant, and mostly giant gas planets.

In short: If you look at a white dwarf, there is a 97% chance it is a lonely ghost star, and only a 3% chance it still has a giant planet orbiting far away in the dark.

Technical Summary: Predicted Incidence of Jupiter-like Planets around White Dwarfs

Problem Statement
While thousands of exoplanets are confirmed around main-sequence stars, and theoretical models suggest that planets with orbits beyond a few astronomical units should survive the host star's evolution into a white dwarf (WD), observational evidence remains scarce. Despite high-contrast imaging surveys and transit searches, only a handful of substellar companions to WDs have been detected. It is currently unclear whether this paucity reflects observational limitations or the actual consequences of stellar evolution (e.g., engulfment during giant phases, tidal interactions, or mass loss). Previous population synthesis studies have been limited by generic assumptions regarding planet populations and a lack of dependency on specific WD parameters such as age and mass. This study aims to fill this gap by performing a detailed population synthesis to predict the fraction and properties of WDs hosting substellar companions.

Methodology
The authors employed a multi-stage population synthesis approach combining stellar evolution codes with orbital dynamics algorithms:

Progenitor Generation: A representative population of 243,617 potential WD progenitors was generated using the Kroupa initial mass function (0.8–4 $M_{\odot}$ ). Stellar ages were assigned assuming a constant star formation rate over a 10 Gyr thin disk, while metallicities were derived from a global age-metallicity relation (Carrillo et al. 2023).
Companion Assignment: Substellar companions (0.8–30 $M_J$ ) were assigned to progenitors based on occurrence rates derived from radial-velocity surveys of giant stars (Wolthoff et al. 2022). The occurrence rate was modeled as a function of stellar mass and metallicity, with orbital periods following a log-normal distribution and eccentricities based on recent exoplanet statistics (Kane & Wittenmyer 2024).
Stellar and Orbital Evolution:
- Stellar Evolution: The majority of the sample was evolved using the Single Star Evolution (SSE) code to determine the present-day WD population. A subset of 1,000 systems initially hosting companions was re-simulated using the Modules for Experiments in Stellar Astrophysics (MESA) to capture detailed physics, particularly thermal pulses and mass loss on the Asymptotic Giant Branch (AGB).
- Orbital Dynamics: The FATES (Final exoplAnet orbiTal dEstination around evolved Stars) algorithm was used to integrate the orbital evolution of companions. This code accounts for orbital expansion due to isotropic stellar mass loss and orbital decay due to stellar tides.
- Uncertainty Testing: The study tested sensitivity to various physical prescriptions, including two different convective turnover timescale models for tidal forces (Rasio et al. 1996 [R96] vs. Villaver & Livio 2009 [VL09]), different AGB mass-loss efficiencies (Bloecker 1995 with $\eta=0.02$ and $\eta=0.7$ ), and alternative age-metallicity relations (Fernández-Alvar et al. 2025).

Key Results
The simulations yield the following quantitative predictions for the current population of WDs in the Milky Way:

Occurrence Rate: The predicted fraction of WDs hosting substellar companions is low, estimated at below 3 ± 1.5 %. This figure is robust across uncertainties in initial distributions, stellar tides, and AGB mass loss.
- Under the assumption of weak tidal forces (VL09), the rate is ~1.3%.
- Under strong tidal forces (R96), the rate drops to ~0.6%.
- If tidal forces are ignored entirely (mass loss only), the rate rises to 3.2%, representing a strict upper limit.
Companion Nature: Approximately 95% of the surviving companions are predicted to be gas-giant planets (masses < 13 $M_J$ ). The general occurrence rate for Jupiter-like planets specifically is below 2.9 ± 1.4 %.
Orbital Properties: Surviving companions are predicted to have semimajor axes ranging from 3 to 24 au, with a median of 11 au. The final orbits are generally wider than initial orbits due to mass loss, though tidal forces can circularize eccentric orbits.
Host Star Characteristics: The occurrence rate peaks for low-mass WDs (0.53–0.66 $M_{\odot}$ ) and relatively young systems (1–6 Gyr), where the rate can exceed 3%.
Dependence on Metallicity and Local Environment: The predictions are highly sensitive to the assumed age-metallicity relation. While the global prediction remains below 3%, applying a local age-metallicity relation (Fernández-Alvar et al. 2025) suggests the fraction of WDs with companions near the Sun could reach < 8 %.

Significance and Conclusions
The authors conclude that if the companion distributions derived from radial-velocity surveys of intermediate-mass giant stars accurately reflect the true population, less than 3 ± 1.5 % of white dwarfs host substellar companions. This suggests that such companions are intrinsically rare.

The paper emphasizes that this low fraction likely represents an upper limit on detectable companions. A significant number of surviving companions may remain undetectable with current facilities due to their wide separations and the faintness of the systems. The study highlights that the survival of companions is critically dependent on the strength of stellar tides and the efficiency of mass loss during the AGB phase. Furthermore, the results underscore that the assumed age-metallicity relation significantly influences predictions, particularly for local samples.

The authors assert that their findings provide a necessary theoretical baseline for interpreting ongoing and future observational surveys (e.g., with JWST and the ELT). They note that while multi-planetary systems and common-envelope survival scenarios could potentially increase these fractions, the current single-companion model provides a first-order estimate indicating that the scarcity of detected WD companions is likely a real astrophysical phenomenon rather than solely an observational bias.