Analytic Models of Brown Dwarfs and the Substellar Mass Limit
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Bibliographic record
Abstract
We present the analytic theory of brown dwarf evolution and the lower mass limit of the hydrogen burning main-sequence stars and introduce some modifications to the existing models. We give an exact expression for the pressure of an ideal nonrelativistic Fermi gas at a finite temperature, therefore allowing for nonzero values of the degeneracy parameter. We review the derivation of surface luminosity using an entropy matching condition and the first-order phase transition between the molecular hydrogen in the outer envelope and the partially ionized hydrogen in the inner region. We also discuss the results of modern simulations of the plasma phase transition, which illustrate the uncertainties in determining its critical temperature. Based on the existing models and with some simple modification, we find the maximum mass for a brown dwarf to be in the range<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn mathvariant="normal">0.064</mml:mn><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mo>⊙</mml:mo></mml:mrow></mml:msub><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">0.087</mml:mn><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mo>⊙</mml:mo></mml:mrow></mml:msub></mml:math>. An analytic formula for the luminosity evolution allows us to estimate the time period of the nonsteady state (i.e., non-main-sequence) nuclear burning for substellar objects. We also calculate the evolution of very low mass stars. We estimate that ≃ 11% of stars take longer than<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mn mathvariant="normal">1</mml:mn><mml:msup><mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:mrow><mml:mrow><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup></mml:math> yr to reach the main sequence, and ≃ 5% of stars take longer than<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mn mathvariant="normal">1</mml:mn><mml:msup><mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:mrow><mml:mrow><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup></mml:math> yr.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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