The non-uniform expansion of the Crab Nebula
Bibliographic record
Abstract
ABSTRACT We present extensive proper motion measurements of the Crab Nebula made from Canada–France–Hawaii Telescope MegaPrime/MegaCam images taken in 2007, 2016, and 2019. A total of 19974 proper motion vectors with uncertainty ${<} 10$ mas yr$^{-1}$ located over the majority of the Crab Nebula are used to map the supernova remnant’s two-dimensional expansion properties that reflect the dynamics of the original explosion, acceleration of ejecta imparted by spin-down energy from the pulsar, and interaction between the ejecta and surrounding cicumstellar material (CSM). The average convergence date we derive is 1105.5$\pm$0.5 CE, which is 15–35 yr earlier compared to most previous estimates. We find that it varies as a function of position angle around the nebula, with the earliest date and smallest proper motions measured along the equator defined by the east and west bays. The lower acceleration of material along the equatorial plane may be indicative of the supernova’s interaction with a disc-like CSM geometry. Comparing our measurements to previous analytical solutions of the Crab’s expansion and our own numerical simulation using the moving mesh hydrodynamics code sprout, we conclude that the ejecta have relaxed closer to homologous expansion than expected for the commonly adopted pulsar spin-down age of $\tau \sim 700$ yr and a pulsar wind nebula (PWN) still evolving inside the flat part of the ejecta density profile. These findings provide further evidence that the PWN has reached the outer steep part of the supernova ejecta density profile and escaped the confines of the ejecta shell in some regions.
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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 | 0.001 |
| 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 | 0.000 |
| 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".