Scaling relations for gamma-ray burst afterglow light curves and centroid motion independent of jet structure and dynamics
Bibliographic record
Abstract
ABSTRACT Models for gamma-ray burst afterglow dynamics and synchrotron spectra are known to exhibit various scale invariances, owing to the scale-free nature of fluid dynamics and the power-law shape of synchrotron spectra. Since GRB 170817A, off-axis jet models including a lateral energy structure in the initial outflow geometry have gained in prominence. Here, we demonstrate how the scale invariance for arbitrary jet structure and dynamical stage can be expressed locally as a function of jet temporal light-curve slope. We provide afterglow flux expressions and demonstrate their use to quickly assess the physical implications of observations. We apply the scaling expressions to the Swift X-ray Telescope sample, which shows a spread in observed fluxes, binned by light-curve slope at time of observation, that increases with increasing light-curve slope. According to the scaling relations, this pattern is inconsistent with a large spread in environment densities if these were the dominant factor determining the variability of light curves. We further show how the late deep Newtonian afterglow stage remains scale-invariant but adds distinct spectral scaling regimes. Finally, we show that for given jet structure a universal curve can be constructed of the centroid offset, image size, and ellipticity (that can be measured using very large baseline interferometry) versus observer angle, in a manner independent of explosion energy and circumburst density. Our results apply to any synchrotron transient characterized by a release of energy in an external medium, including supernova remnants, kilonova afterglows, and soft gamma-repeater flares.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| 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".