Supermassive black holes in galactic bulges
Bibliographic record
Abstract
Abstract Growing evidence indicate supermassive black holes (SMBHs) in a mass range of MBH∼ 106–1010 M⊙ lurking in central stellar bulges of galaxies. Extensive observations reveal fairly tight power laws of MBH versus the mean stellar velocity dispersion σ of the host stellar bulge. Together with evidence for correlations between MBH and other properties of host bulges, the dynamic evolution of a bulge and the formation of a central SMBH should be linked. In this Letter, we reproduce the empirical MBH–σ power laws based on our recent theoretical analyses (Lou & Wang; Wang & Lou; Lou, Jiang & Jin) for a self-similar general polytropic quasi-static dynamic evolution of bulges with self-gravity and spherical symmetry, and present a sensible criterion of forming a central SMBH. The key result is , where 2/3 < n < 1 and is a proportional coefficient characteristic of different classes of host bulges. By fitting and comparing several empirical MBH–σ power laws, we conclude that SMBHs and galactic bulges grow and evolve in a coeval manner and most likely there exist several classes of galactic bulge systems in quasi-static self-similar evolution and that to mix them together can lead to an unrealistic fitting. Based on our bulge-SMBH model, we provide explanations for intrinsic scatter in the relation and a unified scenario for the formation and evolution of SMBHs in different classes of host bulges.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".