Toward Precise Constraints on the Growth of Massive Black Holes
Bibliographic record
Abstract
Growth of massive black holes (MBHs) in galactic centers comes mainly from gas accretion during their QSO/AGN phases. In this paper we apply an extended Soltan argument, connecting the local MBH mass function with the time-integral of the QSO luminosity function, to the demography of MBHs and QSOs from recent optical and X-ray surveys, and obtain robust constraints on the luminosity evolution (or mass growth history) of individual QSOs (or MBHs). We find that the luminosity evolution probably involves two phases: an initial exponentially increasing phase set by the Eddington limit and a following phase in which the luminosity declines with time as a power law (with a slope of -1.2--1.3) set by a self-similar long-term evolution of disk accretion. Neither an evolution involving only the increasing phase with a single Eddington ratio nor an exponentially declining pattern in the second phase is likely. The period of a QSO radiating at a luminosity higher than 10% of its peak value is about (2-3)x10^8 yr, during which the MBH obtains ~80% of its mass. The mass-to-energy conversion efficiency is $0.16\pm0.04 ^{+0.05}_{-0}$, with the latter error accounting for the maximum uncertainty due to Compton-thick AGNs. The expected Eddington ratios in QSOs from the constrained luminosity evolution cluster around a single value close to 0.5-1 for high-luminosity QSOs and extend to a wide range of lower values for low-luminosity ones. The Eddington ratios for high luminosity QSOs appear to conflict with those estimated from observations (~0.25) by using some virial mass estimators for MBHs in QSOs unless the estimators systematically over-estimate MBH masses by a factor of 2-4. We also infer the fraction of optically obscured QSOs ~60-80%. Further applications of the luminosity evolution of individual QSOs are also discussed.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| 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".