The Virial Factor and Biases in Single Epoch Black Hole Mass Determinations
Bibliographic record
Abstract
Accurately determining the masses of supermassive black holes is crucial to understand their evolution and the establishment of their relationship with their host galaxy properties. Beyond the local universe, the single epoch mass estimation method provides a simple procedure to estimate black hole masses in large spectroscopic samples of type-1 active galactic nuclei. The method assumes virialized motion of gas in the close vicinity to the active black holes, traced through broad emission lines. However, because of the assumption of a universal virial factor, this procedure has uncertainties associated with the unknown distribution of the gas clouds. Here, using a sample of 39 quasars observed with the VLT/X-shooter spectrograph, we compare alternative estimations of black hole masses determined from the properties of the accretion disk emission around the black hole with the single epoch virial mass estimations. We find that the virial factor is inversely proportional to the observed width of the broad emission lines. This result implies that current virial masses can be miss-estimated by up to a factor of 6. Our analysis indicates that either the effect of line-of-sight inclination in a planar distribution of the broad line emitting gas or the radiation pressure perturbations to the distribution of gas can reproduce our findings.
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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 | 0.021 | 0.110 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".