Recombinations to the Rydberg states of hydrogen and their effect during the cosmological recombination epoch
Bibliographic record
Abstract
In this paper we discuss the effect of recombinations to highly excited states (n > 100) in hydrogen during the cosmological recombination epoch. For this purpose, we developed a new ordinary differential equation solver for the recombination problem, based on an implicit Gear's method. This solver allows us to include up to 350 l-resolved shells or ∼61 000 separate levels in the hydrogen model and to solve the recombination problem for one cosmology in ∼27 h. This is a huge improvement in performance over our previous recombination code, for which a 100-shell computation (5050 separate states) already required ∼150 h on a single processor. We show that for 350 shells down to redshift z∼ 200, the results for the free electron fraction have practically converged. The final modification in the free electron fraction at z∼ 200 decreases from about ΔNe/Ne∼ 2.8 per cent for 100 shells to ΔNe/Ne∼ 1.6 per cent for 350 shells. However, the associated changes in the cosmic microwave background power spectra at large multipoles l are rather small, so that for accurate computations in connection with the analysis of Planck data already ∼100 shells are expected to be sufficient. Nevertheless, the total value of τ could still be affected at a significant level. We also briefly investigate the effect of collisions on the recombination dynamics. With our current estimates for the collisional rates we find a correction of ΔNe/Ne∼−8.8 × 10−4 at z∼ 700, which is mainly caused by l-changing collisions with protons. Furthermore, we present results on the cosmological recombination spectrum, showing that at low frequencies collisional processes are important. However, the current accuracy of collisional rates is insufficient for precise computations of templates for the recombination spectrum at ν≲ 1 GHz, and also the effect of collisions on the recombination dynamics suffers from the uncertainty in these rates. Improvements in collisional rates will therefore become necessary in order to obtain a final answer regarding their effects during recombination.
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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 | 0.003 |
| 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 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".