Bibliographic record
Abstract
We derive the equations for the propagation of relativistic ionization fronts in both static and moving gases. We focus on the supersonic R-type phase that occurs right after a source turns on, and we compare the nonrelativistic and relativistic solutions for several important cases. Relativistic corrections can be significant up until the light-crossing time of the equilibrium Stromgren sphere. For a static medium, we obtain exact analytical solutions and apply them to the illustrative problems of an O star in a molecular cloud and a starburst in a high-redshift cosmological halo. Relativistic corrections can be important at early times when the H II regions are small, as well as at later times, if a density gradient causes the I-front to accelerate. For the cosmologically-expanding IGM, we derive an analytical solution in the case of a steady source and a constant clumping factor. Here relativistic corrections are significant for short-lived, highly-luminous sources like QSOs at the end of reionization, but negligible for weaker or higher-redshift sources. Finally, we numerically calculate the evolution of relativistic I-fronts in the presence of small-scale structure and infall, for a large galaxy undergoing a starburst and a luminous, high-redshift QSO. For such strong and short-lived sources, the relativistic corrections are quite significant, and small-scale structure can decrease the size of the H II region by up to an additional ~25%. (abridged)
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".