Exploring higher order images with Fe <i>K</i>α-lines from relativistic discs: black hole spin determination and bias
Bibliographic record
Abstract
ABSTRACT We study the contributions to the relativistic Fe K α line profile from higher order images (HOIs) produced by strongly deflected rays from the disc which cross the plunging region, located between the innermost stable circular orbit (ISCO) radius and the event horizon of a Kerr black hole. We investigate the characteristics features imprinted by the HOIs in the line profile for different black hole spins, disc emissivity laws, and inclinations. We find that they extend from the red wing of the profile up to energies slightly lower than those of the blue peak, adding ∼0.4–1.3 per cent to the total line flux. The contribution to the specific flux is often in the ∼1 to 7 per cent range, with the highest values attained for low and negative spin (a ≲ 0.3) black holes surrounded by intermediate inclination angle (i ∼ 40°) discs. We simulate future observations of a black hole X-ray binary system with the Large Area Detector of the planned X-ray astronomy enhanced X-ray Timing and Polarimetry Mission (eXTP) and find that the Fe Kα line profiles of systems accreting at ≲1 per cent the Eddington rate are affected by the HOI features for a range of parameters. This would provide evidence of the extreme gravitational lensing of HOI rays. Our simulations show also that not accounting for HOI contributions to the Fe Kα line profile may systematically bias measurements of the black hole spin parameter towards values higher by up to ∼0.3 than the inputted ones.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".