Constraining the initial entropy of directly-detected exoplanets
Bibliographic record
Abstract
The post-formation, initial entropy S_i of a gas giant planet is a key witness to its mass-assembly history and a crucial quantity for its early evolution. However, formation models are not yet able to predict reliably S_i, making unjustified the use solely of traditional, 'hot-start' cooling tracks to interpret direct imaging results and calling for an observational determination of initial entropies to guide formation scenarios. Using a grid of models in mass and entropy, we show how to place joint constraints on the mass and initial entropy of an object from its observed luminosity and age. This generalises the usual estimate of only a lower bound on the real mass through hot-start tracks. Moreover, we demonstrate that with mass information, e.g. from dynamical stability analyses or radial velocity, tighter bounds can be set on the initial entropy. We apply this procedure to 2M1207 b and find that its initial entropy is at least 9.2 kB/baryon, assuming that it does not burn deuterium. For the planets of the HR 8799 system, we infer that they must have formed with S_i > 9.2 kB/baryon, independent of uncertainties about the age of the star. Finally, a similar analysis for beta Pic b reveals that it must have formed with S_i > 10.5 kB/baryon, using the radial-velocity mass upper limit. These initial entropy values are respectively ca. 0.7, 0.5, and 1.5 kB/baryon higher than the ones obtained from core accretion models by Marley et al., thereby quantitatively ruling out the coldest starts for these objects and constraining warm starts, especially for beta Pic b.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".