THE EXTREME SPIN OF THE BLACK HOLE IN CYGNUS X-1
Bibliographic record
Abstract
The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a * > 0.95 (3σ). For a less probable (synchronous) dynamical model, we find a * > 0.92 (3σ). In our analysis, we include the uncertainties in black hole mass, orbital inclination angle, and distance, and we also include the uncertainty in the calibration of the absolute flux via the Crab. These four sources of uncertainty totally dominate the error budget. The uncertainties introduced by the thin-disk model we employ are particularly small in this case given the extreme spin of the black hole and the disk's low luminosity.
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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 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".