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Constraining the lives and times of exoplanets through evolutionary Bayesian retrievals

This paper introduces a novel evolutionary Bayesian retrieval framework integrated with the PROTEUS multi-physics model to overcome the limitations of static analyses, enabling the simultaneous inference of exoplanets' deep interior structures, volatile histories, and formation conditions from current spectroscopic observations.

Original authors: Harrison Nicholls, Tim Lichtenberg, Ben Riegler, Robb Calder, Vincent Fortuin

Published 2026-07-29

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CC BY 4.0

Original authors: Harrison Nicholls, Tim Lichtenberg, Ben Riegler, Robb Calder, Vincent Fortuin

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 universe as a giant, cosmic library where every book is a planet. For decades, astronomers have been trying to read these books, but they've only been able to see the cover and the very last page. They know how big the planets are, how heavy they feel, and what their current atmospheres smell like. But the real story—the messy, dramatic history of how these worlds formed, how they cooled down, and how they lost their atmospheres over billions of years—has been hidden. This is the realm of exoplanet science, the study of worlds orbiting stars other than our Sun. The big challenge is that many different histories can lead to the same final cover. A planet could look like a "Super-Earth" (a big, rocky world) because it was born that way, or because it started as a "Sub-Neptune" (a gas-rich world) and had its atmosphere stripped away by its star. Without knowing the history, scientists are stuck guessing which story is true.

This paper, titled "Constraining the lives and times of exoplanets through evolutionary Bayesian retrievals," is like inventing a new kind of time machine for those library books. The authors, led by Harrison Nicholls, realized that looking at a planet as a static snapshot is like trying to understand a person's life by looking at a single photo. You can't tell if they are a baby, a teenager, or an elder, or what they ate for breakfast. Instead, they built a new framework called PROTEUS that simulates a planet's entire life story, from its fiery, molten birth to its cool, present-day state. They then used a clever mathematical trick called "Bayesian optimisation" to run thousands of these life simulations at once, searching for the specific story that matches the "photo" we see today. The result? They found that for some types of planets, this time-travel approach can reveal secrets about their deep interiors and ancient atmospheres that were previously impossible to guess, though for others, the mystery remains a bit foggy.

The Problem: The "Where's Waldo?" of Planets

Think of trying to figure out what's inside a sealed, opaque box just by weighing it and measuring its size. If you have a box that weighs 5 kilograms and is the size of a basketball, it could be filled with lead, or it could be a hollow shell filled with feathers. In the world of exoplanets, this is called a "degeneracy." A planet with a thick, fluffy hydrogen atmosphere might look exactly the same size and weight as a planet with a tiny, dense iron core and a thin atmosphere.

For a long time, scientists have used "static retrieval" methods. This is like taking a photo of the planet today and trying to reverse-engineer its interior based only on that single moment. It's a bit like trying to guess the ingredients of a cake by tasting the frosting on a single slice. You might get the flavor right, but you won't know if the baker used a secret ingredient or if the cake was baked for an hour or ten hours. The paper argues that this static approach is prone to getting stuck in "degenerate scenarios"—multiple different histories that all fit the current data equally well, leaving scientists unsure of the truth.

The Solution: A Time-Traveling Detective

The authors decided to stop looking at the planet as a frozen moment and start treating it as a movie. They used a powerful simulation framework called PROTEUS (Planetary Evolution and Atmosphere Simulator). Imagine PROTEUS as a super-advanced video game engine that doesn't just render a planet; it simulates its entire life cycle. It starts the planet as a glowing, molten ball of rock and metal (a "magma ocean") and then runs the clock forward, billions of years at a time.

As the simulation runs, it calculates how the planet cools, how its magma ocean solidifies, how gases bubble up from the deep interior (outgassing), and how the star's radiation strips away the atmosphere. It's a complex dance of physics: the interior heats the atmosphere, the atmosphere traps heat, and the star tries to blow the atmosphere away.

To make this work, they needed a way to find the exact movie that matches the real planet we see today. This is where Asynchronous Bayesian Optimisation (ABO) comes in. Think of ABO as a team of super-smart detectives working in parallel. Instead of checking one story at a time (which would take forever), they dispatch hundreds of simulations simultaneously. As soon as one simulation finishes, the system immediately sends out a new one based on what it learned from the last batch. It's like a "choose your own adventure" book where the story branches out in the most promising directions, quickly narrowing down the possibilities to find the one path that leads to the correct ending.

The Test Drive: Three Planetary Prototypes

To see if their time-travel method worked, the team created three "ground-truth" scenarios—fake planets with known histories—and then tried to use their new method to figure out those histories without knowing them beforehand.

The Young Sub-Neptune (SN): This is a young, puffy planet with a thick atmosphere, similar to the "gas dwarf" type.
The Older Super-Earth (SE): This is an older, rocky planet that has lost most of its atmosphere, sitting in the "radius valley" (the gap between small rocky planets and big gas planets).
The Warm Terrestrial (TR): This is an Earth-sized planet, but hotter and younger, with a rocky surface.

The team ran their ABO detectives on these three cases to see if they could recover the "true" ingredients: the planet's core size, its initial water and gas supply, and the chemical "redox" state (how oxidized or reduced the interior is).

The Results: Successes and Stumbles

The results were a mix of triumphs and lingering mysteries, depending on the type of planet.

The Terrestrial Success Story:
For the warm, Earth-sized planet (TR), the method was a home run. Because this planet's history involves complex changes—like its magma ocean solidifying and changing the atmosphere's composition over time—the "movie" had a unique fingerprint. The ABO detectives were able to reconstruct the planet's initial water and carbon budgets with less than 20 percent error. They even figured out the size of the metal core and the chemical state of the mantle. The paper suggests that for these types of planets, the link between their current atmosphere and their deep history is strong enough that the time-travel method can lift the "degeneracy" and tell us exactly what happened.

The Sub-Neptune and Super-Earth Struggles:
However, for the puffy Sub-Neptune (SN) and the older Super-Earth (SE), the story was different. These planets are still stuck in a bit of a "Where's Waldo?" situation.

The Sub-Neptune: The simulation found that the planet's current size and atmosphere could be explained by many different combinations of core size and initial gas. The method could accurately guess the sulfur content, but it struggled to pin down the exact size of the core or the total amount of hydrogen. The paper notes that the planet's reducing (oxygen-poor) interior makes it outgas hydrogen so efficiently that the atmosphere looks the same regardless of the exact starting conditions.
The Super-Earth: This planet is in a regime where the atmosphere is constantly being eroded by the star. The simulation showed that while the method could guess the chemical state of the mantle, it still couldn't perfectly separate the size of the core from the amount of atmosphere left. It's a classic case of two different histories leading to the same final look.

What This Means for the Future

The paper doesn't claim to have solved the mystery of every exoplanet. Instead, it suggests that evolutionary retrievals (looking at the whole life story) are a powerful new tool that can break some of the deadlocks that have plagued static models.

The authors emphasize that for certain planets—specifically those that are rocky and have gone through significant chemical changes over time—this method can reveal their "deep interiors" and "lifetime histories" with much greater confidence. It allows scientists to say, "This planet must have started with this much water," rather than just guessing.

However, they are careful to note that for some planets, like the gas-rich Sub-Neptunes, the physics is still too tricky, and the "degeneracies" (the multiple possible answers) remain. The paper suggests that while this isn't a magic wand that solves everything, it is a massive step forward. It turns the search for exoplanet secrets from a game of guessing based on a snapshot into a forensic investigation of a full life story.

With upcoming telescopes like JWST, PLATO, and the Roman Space Telescope set to flood us with new data, the authors argue that we need these time-traveling models more than ever. They are the key to turning a pile of numbers and spectra into a coherent history of the worlds around us, helping us understand not just what planets are, but how they came to be.

Technical Summary: Constraining the lives and times of exoplanets through evolutionary Bayesian retrievals

Problem Statement
Current exoplanet characterization relies heavily on static retrieval frameworks that interpret observations as time-independent snapshots. While effective for inferring present-day atmospheric compositions and bulk properties, these models suffer from significant degeneracies. They fail to resolve the evolutionary histories of planets, leaving the internal structures and formation conditions of super-Earths and sub-Neptunes ambiguous. For instance, observed bulk densities can be explained by multiple degenerate scenarios (e.g., steam atmospheres with small metal cores versus extended hydrogen atmospheres over dense interiors). Furthermore, static models often permit physically unachievable scenarios because they lack the constraints imposed by long-term physical processes, such as magma ocean solidification, volatile outgassing, and atmospheric escape over gigayear timescales.

Methodology
The authors introduce a generalized parameter retrieval framework that integrates planetary evolution simulations directly into the inference process, moving beyond the static paradigm. The core of this approach involves:

The PROTEUS Framework: A multi-physics forward model that simulates the coupled thermal and compositional evolution of low-mass rocky bodies from an initial magma ocean state to the present day. PROTEUS self-consistently tracks the metallic core, silicate mantle, and atmosphere, incorporating:
- Interior Dynamics: Mantle geodynamics, magma ocean solidification (using boundary-layer theory for sub-Neptunes), and radiogenic heating.
- Atmosphere-Interior Coupling: Volatile partitioning between the molten mantle and atmosphere via the CALLIOPE module, which solves for equilibrium thermochemical solubility based on temperature and mantle redox conditions ( $\Delta IW$ ).
- Atmospheric Physics: A radiative-convective climate model (AGNI) and hydrodynamic atmospheric escape (via the MORS module) driven by stellar XUV flux.
- Chemistry: Thermochemical equilibrium calculations for major volatile species (H-C-N-S-O).
Asynchronous Bayesian Optimisation (ABO): To overcome the computational expense of running PROTEUS (which can take minutes to hours per simulation), the authors employ ABO. Unlike synchronous batch processing, ABO dispatches simulations asynchronously across multiple CPU cores, minimizing idle time. The algorithm uses a Gaussian Process (GP) surrogate model to approximate the objective function (the deviation between simulated and observed quantities) and an acquisition function (specifically LogEI) to propose the next set of input parameters to evaluate. This allows for efficient exploration of high-dimensional parameter spaces without requiring analytical gradients.
Retrieval Targets: The framework attempts to infer "Class P2" parameters (initial volatile inventories, mantle redox state, and core fraction) from "Class O1" observables (photospheric radius, temperature, gravity, molecular weight, and elemental ratios like C/O, S/O, O/H).

Key Contributions

Development of an Evolutionary Retrieval Framework: The paper presents the first implementation of asynchronous Bayesian optimisation to dispatch a computationally expensive, multi-physics planetary evolution model (PROTEUS) for parameter retrieval.
Resolution of Degeneracies: By constraining the retrieval to physically permissible evolutionary pathways, the framework lifts degeneracies inherent in static models, particularly for terrestrial-mass planets.
Comparative Analysis: The study provides a direct comparison between the new evolutionary retrieval and a state-of-the-art static retrieval framework (InferAGNI), highlighting differences in inferred surface conditions and interior structures.
Algorithmic Benchmarking: The authors systematically evaluate different acquisition functions (UCB, LogPI, LogEI), Gaussian process kernels (RBF, Matérn), and worker parallelization strategies to optimize retrieval performance.

Results
The authors tested the framework on three synthetic exoplanet prototypes: a young Sub-Neptune (SN), an older Super-Earth (SE), and a warm Terrestrial (TR).

Terrestrial Case (TR): The evolutionary retrieval achieved the highest performance, recovering post-formation volatile inventories with $\lesssim 20\%$ error. Strong correlations between observables and parameters in the oxidized terrestrial regime allowed the framework to accurately infer the initial hydrogen inventory, carbon-to-hydrogen ratio, and core fraction, effectively lifting the mass-radius degeneracy.
Sub-Neptune Case (SN): The retrieval successfully inferred the initial sulfur budget by linking it to the observed atmospheric S/O ratio. However, the framework struggled to accurately constrain the core fraction and initial volatile budget due to the "reducing" interior conditions, which generate H $_2$ -dominated atmospheres insensitive to compositional variations. This case exhibited the same core-fraction/volatility degeneracy found in static retrievals.
Super-Earth Case (SE): The retrieval converged on the ground-truth photospheric radius but struggled with the core fraction and initial volatile budget. The planet's susceptibility to photoevaporative carbon depletion created complex evolutionary pathways, leading to a preference for low-density interiors in the retrieval.
Static vs. Evolutionary: Evolutionary retrievals provided greater physical insight into surface conditions (pressure-temperature states). Static retrievals often explored cooler, higher-pressure regimes that were physically inconsistent with the evolutionary history of a molten planet, whereas the evolutionary framework naturally disfavored unphysical states (e.g., retaining massive low-metallicity atmospheres on small planets for billions of years).
Optimization: The LogEI acquisition function with a Matérn kernel ( $\nu=5/2$ ) and 3–5 parallel workers proved most effective, converging to high-fidelity solutions within approximately 60–70 PROTEUS evaluations.

Significance and Claims
The paper claims that exoplanet science is "primed" for the integration of time-evolved models to interpret incoming data from JWST, PLATO, Roman, and ELT. The primary significance lies in the ability to:

Lift Interpretive Degeneracies: By incorporating the physics of planetary evolution, the framework restricts solutions to physically permissible scenarios, offering a more robust interpretation of deep interiors and lifetime histories.
Infer Hidden Parameters: The method enables the joint inference of mantle redox states and early volatile inventories (H, C, S) from spectroscopically accessible observables, parameters that are otherwise inaccessible to static models.
Feasibility: The study demonstrates that computationally expensive evolutionary retrievals are feasible within a modest computational budget (fewer than 10 CPU cores, hours of wall-clock time), making them a viable successor to the static retrieval paradigm for characterizing the diverse population of exoplanets.

The authors remain modest, acknowledging that evolutionary retrievals are not a "panacea"; degeneracies persist in specific regimes (e.g., reducing sub-Neptunes), and the efficacy depends heavily on the specific physical regime of the target planet. However, the framework provides a necessary step toward understanding the deep interiors and formation histories of worlds throughout the galaxy.

The Problem: The "Where's Waldo?" of Planets

The Solution: A Time-Traveling Detective

The Test Drive: Three Planetary Prototypes

The Results: Successes and Stumbles

What This Means for the Future

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