TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. IV. RELATIVISTICALLY BROADENED IRON LINES
Bibliographic record
Abstract
According to the no-hair theorem, astrophysical black holes are fully characterized by their masses and spins and are described by the Kerr metric. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we calculate the profiles of fluorescent iron lines emitted from the accretion flows around black hole candidates within a framework that allows us to perform the calculation as a function of its mass and spin as well as of a free parameter that measures potential deviations from the Kerr metric. We show that such deviations lead to line profiles that are significantly altered and may exhibit a modified flux ratio of the two peaks in their characteristic double-peaked shape. We also show that the disk inclination can be measured independently of the spin and the deviation parameter at low to intermediate inclination angles as in the case of Kerr black holes. We estimate the precision that near-future X-ray missions such as Astro-H and ATHENA+ are required to achieve in order to resolve deviations from the Kerr metric in iron line profiles and show that constraints on such deviations will be strongest for rapidly spinning black holes. More generally, we show that measuring the line profile with a precision of ~5% at disk inclinations of 30 or 60 degrees constraints the deviation parameter to order unity for values of the spin a>0.5M.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 teacher head, 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".