Thermalization in Relativistic Outflows and the Correlation between Spectral Hardness and Apparent Luminosity in Gamma‐Ray Bursts
Bibliographic record
Abstract
We present an interpretation of the phenomenological relations between the spectral peak, isotropic luminosity and duration of long gamma ray bursts that have been discovered by Amati et al., Ghirlanda et al., Firmani et al., and Liang & Zhang. In our proposed model, a jet undergoes internal dissipation which prevents its bulk Lorentz factor from exceeding 1/theta (theta being the jet opening angle) until it escapes from the core of its progenitor star, at a radius of order 1e10 cm; dissipation may continue at larger radii. The dissipated radiation will be partially thermalized, and we identify its thermal peak (Doppler boosted by the outflow) with E_pk. The radiation comes, in effect, from within the jet photosphere. The non-thermal, high energy part of the GRB emission arises from Comptonization of this radiation by relativistic electrons and positrons outside the effective photosphere. This model can account naturally not only for the surprisingly small scatter in the various claimed correlations, but also for the normalization, as well as the slopes. It then has further implications for the jet energy, the limiting jet Lorentz factor, and the relation of the energy, opening angle and burst duration to the mass and radius of the stellar stellar progenitor. The observed relation between pulse width and photon frequency can be reproduced by inverse-Compton emission at ~ 1e14 cm from the engine, but there are significant constraints on the energy distribution and isotropy of the radiating particles.
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How this classification was reachedexpand
Full frame distilled prediction
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 | 0.001 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".