The Fundamental Plane of Black Hole Accretion and Its Use as a Black Hole-Mass Estimator
Bibliographic record
Abstract
Abstract We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole (M), its 5 GHz radio continuum luminosity (νL ν ), and its 2–10 keV X-ray power-law continuum luminosity (L X ). We compile a sample of black holes with primary, direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a mass-predictor function of the form log ( M / 10 8 M ⊙ ) = μ 0 + ξ μ R log ( L R / 10 38 erg s − 1 ) + ξ μ X log ( L X / 10 40 erg s − 1 ) . Our best-fit results are μ 0 = 0.55 ± 0.22, ξ μR = 1.09 ± 0.10, and ξ μ X = − 0.59 − 0.15 + 0.16 with the natural logarithm of the Gaussian intrinsic scatter in the log-mass direction ln ϵ μ = − 0.04 − 0.13
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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 | 0.006 | 0.038 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".