Optical depth estimates and effective critical densities of dense gas tracers in the inner parts of nearby galaxy discs
Bibliographic record
Abstract
High critical density molecular lines like HCN (1-0) or HCO+ (1-0) represent our best tool to study currently star-forming, dense molecular gas at extragalactic distances. The optical depth of these lines is a key ingredient to estimate the effective density required to excite emission. However, constraints on this quantity are even scarcer in the literature than measurements of the high-density tracers themselves. Here, we combine new observations of HCN, HCO+ and HNC (1-0) and their optically thin isotopologues H13CN, H13CO+ and HN13C (1-0) to measure isotopologue line ratios. We use IRAM 30-m observations from the large programme EMPIRE and new Atacama Large Millimetre/submillimetre Array observations, which together target six nearby star-forming galaxies. Using spectral stacking techniques, we calculate or place strong upper limits on the HCN/H13CN, HCO+/H13CO+ and HNC/HN13C line ratios in the inner parts of these galaxies. Under simple assumptions, we use these to estimate the optical depths of HCN (1-0) and HCO+ (1-0) to be τ ∼ 2–11 in the active, inner regions of our targets. The critical densities are consequently lowered to values between 5 and 20 × 105 cm−3, 1 and 3 × 105 cm−3 and 9 × 104 cm−3 for HCN, HCO+ and HNC, respectively. We study the impact of having different beam-filling factors, η, on these estimates and find that the effective critical densities decrease by a factor of |$\frac{\eta _{12}}{\eta _{13}}\,\tau _{12}$|. A comparison to existing work in NGC 5194 and NGC 253 shows the HCN/H13CN and HCO+/H13CO+ ratios in agreement with our measurements within the uncertainties. The same is true for studies in other environments such as the Galactic Centre or nuclear regions of active galactic nucleus dominated nearby galaxies.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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".