Evolutionary tracks of giant planets formed by disk instability

arXiv:2608.11984 · astro-ph.EP · Submitted 2026-08-12 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. The week's best astrophysics papers, unpacked for curious ears.

Vera: Next we'll be talking about the paper "Evolutionary tracks of giant planets formed by disk instability".

Jocelyn: The paper was written by Mirco Bussmann and Ravit Helled from University of Zürich.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Paper discussion segment 1: Vera: Back to the paper "Evolutionary tracks of giant planets formed by disk instability" by Mirco Bussmann and Ravit Helled in Zürich. We’ve covered the broad strokes, but what I find genuinely exciting is how they treat the whole life of the clump — from a puffy, cold object a few astronomical units across, down to a compact giant planet cooling over billions of years. They don’t just pick a hot or cold starting point; they simulate the pre-collapse phase with dust opacities down to ten kelvin, which is well below what MESA normally handles.

Jocelyn: That jump from a few astronomical units to two or three Jupiter radii is dramatic. They say the dynamical collapse itself lasts only about the free-fall timescale, a few years, and they don’t model it directly — they assume adiabatic collapse and match the total entropy before and after. The central temperature hits roughly two thousand kelvin when molecular hydrogen starts dissociating, and that’s what pulls the rug out from under pressure support. So the post-collapse radius is basically set by entropy conservation.

Vera: And they switch equations of state at that moment — SCvH for the cold clump, CMS for the hot collapsed planet. There’s a subtlety: the two EoS give initial radii that differ by up to fifty percent for the same entropy, but they test that and find the difference disappears after about a million years. What actually matters for the long-term cooling is the EoS choice itself, not the transient radius mismatch. That’s a careful robustness check.

Subrahmanyan: The striking implication, and I think the core of “Evolutionary tracks of giant planets formed by disk instability,” is that disk instability can’t be ruled out by current luminosity observations. They match dynamical masses for HR eight thousand seven hundred ninety-nine e, AF Lep b, β Pic b and β Pic c. But they also show that hot-accretion core accretion models produce almost identical cooling curves beyond a few million years. So luminosity alone becomes a very weak discriminator of formation pathway.

Jocelyn: That’s where metallicity sneaks in and complicates the mass estimates. They ran models at zero point five, one, and two times protosolar metallicity, and for a given age and luminosity, the inferred mass can vary by up to one point five Jupiter masses — most severely for massive planets at ages of a few tens of millions of years, which is exactly the regime of directly imaged planets. So an observer assuming solar composition could systematically bias the mass by a Jupiter mass or more.

Vera: I like that they quantify this with synthetic observations in their Table one — for a forty-million-year-old planet with a given luminosity, the inferred mass shifts from about nine point seven Jupiter masses at two times protosolar metallicity to over eleven Jupiter masses at half protosolar. That’s a huge degeneracy. It means future work needs better constraints on planetary composition, maybe from atmospheric spectroscopy, before we can really nail down masses from cooling tracks alone.

Subrahmanyan: And yet the paper is cautiously optimistic. They note that cold accretion models with low-mass cores stay distinct for a long time, while models with massive cores converge to the disk-instability tracks quite early. That suggests the initial entropy, not the formation mechanism per se, controls what we see. The authors close by pointing to Gaia Data Release four later this year for more dynamical masses, which will give this framework a much larger benchmark set to test against.

Jocelyn: It’s a useful reminder that “hot start” and “cold start” are oversimplifications. Their disk-instability objects are hot, sure, but the exact entropy depends on mass and metallicity. And the age of the system is often the dominant uncertainty — for AF Lep b, switching from a dynamical age of about eighteen point five million years to an isochronal age of twenty-four million years pushes the inferred mass above the dynamical measurement. So model and observation both have to come together.

Vera: Absolutely. This paper gives us a self-consistent framework, and the next step is more benchmark planets. For now, the headline from “Evolutionary tracks of giant planets formed by disk instability” is that disk instability remains a live option, but only if we take composition seriously. We’ll be back after the break with listener questions on how these tracks compare to the Sonora and ATMO models.

Paper discussion segment 2: Vera: We're back with the paper "Evolutionary tracks of giant planets formed by disk instability" by Bussmann and Helled from Zurich. In the first part of our discussion, we watched those cold, extended gas clumps slowly contract until they suddenly collapse into planets. What really matters is what happens after that collapse — and whether those predictions match what we actually see in the sky.

Jocelyn: And that's where the paper gets really interesting, because they take their cooling tracks and apply them to four directly imaged exoplanets with independently measured dynamical masses: HR eight thousand seven hundred ninety-nine e, AF Lep b, β Pic b and β Pic c. For each one, they use the planet's measured luminosity and the system's age to infer a mass from their models, and then they compare that to the mass derived from orbital motion. This is exactly the kind of cross-check you want.

Subrahmanyan: So that's a genuine test — the models have to predict something that observations already know.

Vera: Exactly. For HR eight thousand seven hundred ninety-nine e, they get a model mass between about eight point four and ten point nine Jupiter masses, and the dynamical mass is nine point six with an uncertainty of about one point eight. For AF Lep b, the model gives four point one to six point nine Jupiter masses, and the dynamical mass is three point seven five plus or minus zero point five. And β Pic c comes in at six point two to eight point one Jupiter masses versus eight point three plus or minus one.

Jocelyn: And even β Pic b, which is the most massive and hottest of the four, is consistent — the model only gives a lower limit above eleven point eight five Jupiter masses, while the dynamical mass is nine point three with error bars that reach up to nearly twelve. So every single one of these benchmark planets agrees with the disk instability tracks.

Subrahmanyan: That sounds like a strong statement in favor of disk instability. But I recall the paper also says the opposite — that you can't use luminosity to tell formation mechanisms apart.

Vera: That's the crucial caveat, and it's worth being precise about. The authors compare their tracks to core accretion models with hot accretion, and those are almost indistinguishable from disk instability tracks after a few million years. Even cold accretion models converge to the same curves if the core is massive enough, and that can happen by about ten million years.

Jocelyn: So the same luminosity evolution can be produced by both formation channels. The agreement with dynamical masses means disk instability is still viable, but it doesn't prove that any particular planet formed that way.

Subrahmanyan: Right, you can't do forensics from a cooling curve alone.

Vera: Precisely. And that's why the metallicity part matters so much. They run their models at zero point five, one and two times the protosolar metallicity, and the differences are not small. For a planet at an intermediate age — say forty million years — the same luminosity and age can yield inferred masses that differ by up to one point five Jupiter masses depending on the assumed composition.

Jocelyn: That's a huge systematic uncertainty, especially because many directly imaged planets sit exactly in that age range. The effect is strongest at those intermediate ages, between roughly thirty and sixty million years, while at very young ages the tracks are clustered and at old ages they converge again.

Subrahmanyan: So a metal-rich planet cools slower because the opacity is higher, meaning it stays brighter for longer, and if you assume it has solar composition you'd overestimate its mass.

Vera: You've got it. Higher metallicity means more dust grains, higher opacity, slower cooling. And there's another wrinkle: the pre-collapse phase itself is longer for metal-rich clumps, which delays the start of the post-collapse evolution. Those two effects combine, and the result is that composition can bias mass estimates in a way that's often ignored.

Jocelyn: The authors make a very practical point that anyone who uses age-luminosity relations for young giant planets should take planetary metallicity into account, not just stellar metallicity. The host star's composition doesn't necessarily match the planet's, especially if the clump formed in a spiral arm where metals might be enhanced.

Subrahmanyan: And yet, despite all those uncertainties, their tracks still line up with the four dynamical masses. That gives me some confidence that the basic picture is right, even if the exact mass of any individual planet remains fuzzy.

Vera: And that's the honest conclusion of the paper: disk instability remains a viable formation pathway, the cooling tracks are consistent with established hot-start models like ATMO two thousand twenty and Sonora, but luminosity alone cannot distinguish between formation histories. The next step is more benchmark planets, and the authors point out that Gaia Data Release four at the end of two thousand twenty-six should give us more dynamical masses to test against.

Jocelyn: So the field is moving from just measuring luminosities to actually constraining the physics of formation, but it's going to take a larger sample to break the degeneracies. That's the story of "Evolutionary tracks of giant planets formed by disk instability" in a nutshell.

Paper discussion segment 3: Vera: Back to the paper "Evolutionary tracks of giant planets formed by disk instability" — the real step forward here is that they follow a clump from its extended, cold phase all the way through collapse and cooling in one unified calculation. That hasn't been done before, because previous disk-instability evolution models had to pick an arbitrary starting point after formation.

Jocelyn: So they're actually tracking the pre-collapse time as part of the planet's age, right? That's a big difference from just assuming a hot start at zero time.

Vera: Exactly. And that's why the mass dependence jumps out — they find the pre-collapse phase lasts roughly two hundred sixty thousand years for a one-Jupiter-mass clump, but only about five thousand six hundred years for ten Jupiter masses. The contraction is driven by gravity, and more massive clumps just compress much faster.

Subrahmanyan: That's a huge dynamical range, and it feeds directly into their metallicity results. They ran models at zero point five, one and two times the protosolar metallicity, and for a fixed measured age and luminosity the inferred mass can shift by up to one point five Jupiter masses. That kind of systematic uncertainty had been ignored in most earlier cooling curves.

Jocelyn: And the age at which that matters most is right in the thirty to sixty million year range, which is exactly where many directly imaged planets sit. So when they apply their tracks to HR eight thousand seven hundred ninety-nine e, AF Lep b, β Pic b, and β Pic c, they get masses consistent with dynamical measurements, but the metallicity spread is still large enough to blur the picture.

Vera: I think the key technical improvement is how they handled the equations of state and opacities. They had to add custom low-temperature opacity tables below one hundred kelvin for the pre-collapse phase, and their careful check shows that even a fifty percent difference in the post-collapse radius, depending on which equation of state you pick, disappears within a million years.

Jocelyn: So the long-term evolution is robust to that switch, but the atmospheric boundary condition remains the weak point. Their grey atmosphere is a lot simpler than what the sonora red diamondback models do, and when they compare, clouds and condensation change the cooling at intermediate luminosities until the L/T transition near an effective temperature of roughly one thousand three hundred kelvin.

Subrahmanyan: That's where I see the paper's suggested next steps: they explicitly call for better low-temperature opacities and for folding more realistic atmospheric chemistry into the disk-instability framework. They also point to Gaia Data Release four expected at the end of two thousand twenty-six as a way to get dynamical masses for more directly imaged planets, which will really stress-test these cooling tracks.

Vera: And it's a nice, honest conclusion — the tracks from disk instability look almost identical to core accretion with hot accretion, so luminosity alone can't distinguish the two formation pathways. But the model still predicts masses that agree with every dynamical constraint currently available, so disk instability very much stays on the table.

Jocelyn: That means the next improvement is really observational. More dynamical masses, combined with better constrained ages and compositions, will break the degeneracy that this paper has so carefully quantified.

Subrahmanyan: Agreed. For now, the paper "Evolutionary tracks of giant planets formed by disk instability" gives us a solid framework, a clear sense of where the uncertainties come from, and a roadmap for what we need to measure next.

Paper discussion segment 4: Vera: Welcome back. We’re staying with the paper “Evolutionary tracks of giant planets formed by disk instability” by Mirco Bussmann and Ravit Helled, and I want to slow down on the first page, because the abstract alone packs in a whole argument. Jocelyn, what caught your eye there?

Jocelyn: The very first sentence is the key: the evolution of a giant planet depends on its formation history. And then they spell out the gap — core accretion has all these self-consistent models that tie formation to long-term cooling, but disk instability has never had that kind of unified framework. That’s exactly the hole this paper fills.

Subrahmanyan: And the introduction on that same page gives a nice clue why it matters. They cite the statistic that the host-star metallicity correlation weakens for planets above roughly four Jupiter masses, and those planets tend to orbit more metal-poor stars. That hints that the most massive directly imaged worlds might have a different origin altogether.

Vera: Right, so this paper sets out to simulate the entire life of a disk-instability planet: the extended, low-density clump, the pre-collapse contraction, the dynamical collapse, and then the long-term cooling. They use the MESPA code with masses from one to twelve Jupiter masses and metallicities from half to twice the protosolar value. Those are the numbers that anchor everything else.

Jocelyn: And the abstract’s headline results are concrete. The pre-collapse timescale depends strongly on mass, the collapse happens fast, and then you get billions of years of contraction. But the one that really jumps out is the metallicity effect: for the same measured age and luminosity, the inferred mass can shift by up to one and a half Jupiter masses depending on composition.

Subrahmanyan: That’s a serious systematic for anyone estimating masses of young planets from brightness. And it’s not just theoretical — the paper notes their tracks agree with the dynamical masses for HR eight thousand seven hundred ninety-nine e, AF Lep b, β Pic b, and β Pic c. Those are independent orbital measurements, so it’s a real test, not a toy.

Vera: Yes, and the abstract already foreshadows the uncomfortable conclusion: core accretion and disk instability can produce almost identical long-term luminosity tracks. So even if disk instability passes the observational test, luminosity alone won’t tell you which formation channel created a given planet. The implication is that metallicity becomes essential for accurate mass estimates.

Jocelyn: The introduction on the first page frames it as two populations — the metallicity correlation holds below about four Jupiter masses but breaks down above that, suggesting two formation mechanisms. So the massive, wide-orbit planets are exactly where disk instability has the best shot, and this paper gives the theoretical tracks to compare against.

Subrahmanyan: And there’s a nice physical point buried in that same discussion: in disk instability, the clump forms through self-gravitational binding, so there’s no obvious way to remove entropy — that naturally gives a hot start. Core accretion, on the other hand, can produce cold, warm, or hot starts depending on how accretion energy is radiated. So initial entropy isn’t a clean formation diagnostic either.

Vera: Exactly. The first page of “Evolutionary tracks of giant planets formed by disk instability” lays out the motivation, the method, and the main conclusions in one sweep. We’ll get into the details of the simulations in the next segment, but I think the abstract really does tell the whole story.

Conclusion: Vera: Well Jocelyn, I think we can wrap this one up with a clear picture: Bussmann and Helled have given us the first full evolutionary tracks that take a gas clump from the disk-instability formation stage all the way through collapse and billions of years of cooling.

Jocelyn: And the really encouraging part is that their models line up with the dynamical masses we have for HR eight thousand seven hundred ninety-nine e, AF Lep b, and both β Pic planets. That gives disk instability a solid observational footing.

Vera: But they also throw a bit of cold water on the idea that we can easily tell formation stories apart. It turns out core accretion with hot accretion can produce very similar luminosity evolution, so the light we see from a young giant planet just isn't enough to say which pathway it took.

Jocelyn: Right, and that metallicity effect is a nice warning for anyone trying to turn a luminosity measurement into a mass. If you don't know the planet's composition, your mass estimate could be off by as much as one and a half Jupiter masses, especially around a few tens of millions of years.

Vera: So the takeaway is that disk instability stays on the table as a formation mechanism, but we'll need more than cooling curves to settle the debate. More dynamical masses from upcoming data releases should really help.

Jocelyn: That's a fair place to leave it. We've been discussing "Evolutionary tracks of giant planets formed by disk instability" by Mirco Bussmann and Ravit Helled, and we'll be back shortly with another paper from the arXiv.

Vera: Thanks for listening, and we'll see you in the next segment.

Mirco Bussmann, Ravit Helled

University of Zürich

astro-ph.EP

Submitted: 2026-08-12

Updated: 2026-08-13

Comments: Accepted for publication in A&A, 13 pages, 13 figures

Code: https://github.com/tiny-hippo/tinyeoshttps:

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 48/100

The gist: This paper presents evolutionary tracks for giant planets formed via disk instability, simulated using the MESPA code with modifications to include the extended, low-density gas clumps in the

Key concepts

Disk instability: A planet formation theory where a protoplanetary disk fragments into gravitationally bound clumps that collapse to form giant planets. Unlike core accretion, it can form planets quickly and is a 'hot start' scenario, meaning the planet begins with high entropy and luminosity.
Cooling tracks: Models that predict how a planet's luminosity and radius evolve over time as it cools. These tracks depend on initial entropy, mass, and metallicity, and are used to infer a planet's mass from its observed luminosity and age.
Dynamical mass: A planet's mass measured directly from its gravitational influence, such as the orbital motion of a companion star or the planet itself. These measurements are independent of cooling models and serve as benchmarks to test theoretical predictions.
Metallicity: The abundance of elements heavier than hydrogen and helium. Higher metallicity increases opacity, slowing a planet's cooling and making it appear brighter for longer. This can bias mass estimates if the planet's composition differs from the assumed solar value.

Terminology

Core — 44× in this paper · explained in 2 episodes
Metallicity — 41× in this paper · explained in 3 episodes
Abundance — 2× in this paper · explained in 1 episode
Consistency — 2× in this paper · explained in 3 episodes
Degeneracy — 2× in this paper · explained in 3 episodes
Population Synthesis — 2× in this paper · explained in 2 episodes
Benchmark — 1× in this paper · explained in 2 episodes
Equations of State — 1× in this paper

Summary

This paper presents evolutionary tracks for giant planets formed via disk instability, simulated using the MESPA code with modifications to include the extended, low-density gas clumps in the pre-collapse phase. The evolution is followed through three phases: pre-collapse, dynamical collapse, and long-term contraction, for masses between 1 and 12 Jupiter masses and metallicities ranging from 0.5 to 2 times the protosolar value.

The paper confirms that the pre-collapse timescale strongly depends on planetary mass, with more massive clumps collapsing faster due to greater compression and higher temperatures. The dynamical collapse occurs when central temperatures reach 2000 K, triggering molecular hydrogen dissociation, and the post-collapse objects reach radii of 2 to 3.5 Jupiter radii. The initial post-collapse entropies are very high, similar to classical hot-start models.

The paper shows that metallicity is a major source of uncertainty in mass estimates derived from age–luminosity relations. For a given measurement of age and luminosity, the difference in inferred mass can be up to 1.5 Jupiter masses across the metallicity range considered. The effect of metallicity is strongest at intermediate ages (30–60 Myr), while at very young (60 Myr) the inferred masses are less sensitive to metallicity.

The evolution tracks predict masses consistent with measured dynamical mass constraints for HR 8799 e, AF Lep b, β Pic b, and β Pic c. For HR 8799 e, the inferred mass range is 8.42–10.90 Jupiter masses, consistent with the dynamical mass of 9.6+1.9/−1.8 Jupiter masses. For AF Lep b, the inferred mass range is 4.11–6.94 Jupiter masses, consistent with the dynamical mass of 3.75 ± 0.5 Jupiter masses. For β Pic c, the inferred mass range is 6.21–8.10 Jupiter masses, consistent with the dynamical mass of 8.3 ± 1.0 Jupiter masses. For β Pic b, the inferred mass is above 11.85 Jupiter masses, consistent with the dynamical mass of 9.3+2.6/−2.5 Jupiter masses.

The paper also shows that both core accretion and disk instability can lead to very similar long-term evolutionary tracks, particularly when core accretion models assume hot accretion. Cold accretion models with low-mass cores remain distinct until relatively late times (>10 8 years), while models with massive cores converge much earlier (10 7 years). The luminosity evolution alone cannot distinguish between the two formation pathways.

The conclusions state that the agreement between the models and dynamical mass measurements suggests that disk instability remains a viable formation pathway for giant exoplanets. The paper suggests that planetary metallicity must be taken into account when inferring the masses of young giant planets from their luminosities, as it significantly affects their evolution.

Improvements for AI systems

Improvements to AI Systems Based on This Paper:

Metallicity-Aware Mass Inference for Exoplanet Characterization

Improvement: Train a Bayesian neural network or Gaussian process emulator on the evolutionary tracks (pre-collapse, collapse, post-collapse) that takes planetary mass, age, and metallicity as inputs and outputs luminosity, radius, and entropy.
Capability: Given an observed luminosity and age (with uncertainties), the AI can directly infer a posterior distribution of mass and metallicity simultaneously, avoiding the 1.5 Jupiter-mass systematic error identified in the paper. This is a major upgrade over current tools that assume fixed solar metallicity.

Time-Resolved Phase Classification for Giant Planet Formation

Improvement: Implement a recurrent neural network (LSTM or transformer) trained on the simulated evolutionary tracks to classify which phase a planet is in (pre-collapse, dynamical collapse, or long-term contraction) based on its current radius, luminosity, and central temperature.
Capability: The AI can flag whether an observed young giant planet is still in the pre-collapse phase (extended, low-density) or has already collapsed, enabling astronomers to prioritize targets for follow-up observations (e.g., to catch a collapse event in real time).

Formation Pathway Disambiguation via Multi-Model Comparison

Improvement: Build an ensemble AI that jointly runs disk-instability tracks (from this paper) and core-accretion tracks (hot vs. cold accretion, varying core masses) and uses a mixture-of-experts model to output the probability that a given observed planet formed via each pathway, given its luminosity, age, and dynamical mass constraint.
Capability: The AI can identify the earliest age at which the two pathways become distinguishable (e.g., >10 8 years for cold accretion with low-mass cores, 10 7 years for massive cores), and recommend optimal observational epochs for distinguishing formation history.

Uncertainty-Aware Dynamical Mass Validation

Improvement: Create an AI-driven tool that automatically compares predicted mass ranges (from the evolutionary tracks, including metallicity spread) against measured dynamical masses (e.g., from astrometry or radial velocity) and computes a consistency score, while propagating all uncertainties (age, metallicity, luminosity, dynamical mass).
Capability: The AI can rapidly validate or reject formation models for newly discovered giant planets (like HR 8799 e, AF Lep b, β Pic b/c) and flag cases where the inferred mass range is inconsistent, prompting re-analysis of stellar age or metallicity assumptions.

Metallicity-Dependent Cooling Rate Predictor

Improvement: Train a symbolic regression or neural network to learn the functional form of how metallicity (0.5–2× protosolar) modifies the cooling rate and radius evolution during the long-term contraction phase.
Capability: The AI can provide fast, accurate predictions of a planet's luminosity and radius at any age for arbitrary metallicity, without needing to rerun full MESPA simulations—enabling large-scale population synthesis studies of giant exoplanets.

Early-Collapse Trigger Detector

Improvement: Use the simulated pre-collapse tracks to train a classifier that predicts the exact time and conditions (central temperature 2000 K, molecular hydrogen dissociation) when dynamical collapse will occur, based on initial clump mass, metallicity, and entropy.
Capability: The AI can forecast collapse events for forming planets in protoplanetary disks, helping observers schedule high-cadence monitoring of young systems to capture the rapid radius contraction (from extended clump to 2–3.5 Jupiter radii).

Abstract

The evolution of giant planets depends on their formation history. While several evolutionary models self-consistently link planet formation by core accretion to long-term evolution, such models for planets formed by disk instability are lacking. We simulate the evolution of giant planets formed by disk instability and follow their evolution including the pre-collapse phase, dynamical collapse, and long-term contraction in a unified numerical framework. The evolution is simulated using the MESPA code with modifications that allow us to model gas clumps in the pre-collapse phase. We consider masses between 1 and 12 Jupiter masses and metallicities ranging from 0.5 to 2 times the protosolar value. We confirm that the pre-collapse timescale strongly depends on the planetary mass, and that after dynamical collapse the objects reach a state of long-term contraction which lasts for billions of years. We show that metallicity is a major source of uncertainty in mass estimates derived from the age-luminosity relations. For the metallicity range considered here, we find that for a given measurement of age and luminosity the difference in the inferred mass can be up to 1.5 Jupiter masses. We find that our evolution tracks predict masses that are consistent with the measured dynamical mass constraints for HR 8799 e, AF Lep b, Beta Pic b and Beta Pic c. We also show that both core accretion and disk instability can lead to very similar long-term evolutionary tracks. The agreement between our models and dynamical mass measurements suggests that disk instability remains a viable formation pathway for giant exoplanets. The luminosity evolution alone cannot distinguish between the two formation pathways. Finally, we suggest that planetary metallicity must be taken into account when inferring the masses of young giant planets from their luminosities, as it significantly affects their evolution.