A Comparison of Two Methods for Estimating Black Hole Spin in Active Galactic Nuclei
Bibliographic record
Abstract
Abstract Angular momentum, or spin, is a fundamental property of black holes (BHs), yet it is much more difficult to estimate than mass or accretion rate (for actively accreting systems). In recent years, high-quality X-ray observations have allowed for detailed measurements of the Fe Kα emission line, where relativistic line broadening allows constraints on the spin parameter (the X-ray reflection method). Another technique uses accretion disk models to fit the AGN continuum emission (the continuum-fitting, or CF, method). Although each technique has model-dependent uncertainties, these are the best empirical tools currently available and should be vetted in systems where both techniques can be applied. A detailed comparison of the two methods is also useful because neither method can be applied to all AGN. The X-ray reflection technique targets mostly local (z ≲ 0.1) systems, while the CF method can be applied at higher redshift, up to and beyond the peak of AGN activity and growth. Here, we apply the CF method to two AGN with X-ray reflection measurements. For both the high-mass AGN, H1821+643, and the Seyfert 1, NGC 3783, we find a range in spin parameter consistent with the X-ray reflection measurements. However, the near-maximal spin favored by the reflection method for NGC 3783 is more probable if we add a disk wind to the model. Refinement of these techniques, together with improved X-ray measurements and tighter BH mass constraints, will permit this comparison in a larger sample of AGN and increase our confidence in these spin estimation techniques.
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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 | 0.005 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| 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 | 0.001 |
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".