What Do Statistics Reveal About the <i>M</i><sub>BH</sub>–<i>M</i><sub>bulge</sub> Correlation and Co-Evolution?
Bibliographic record
Abstract
Abstract Observational data show that the correlation between the masses of supermassive black holes MBH and galaxy bulge masses Mbulge follows a nearly linear trend, and that the correlation is strongest with the bulge rather than the total stellar mass Mgal. With increasing redshift, the ratio Γ=MBH/Mbulge relative to z = 0 also seems to be larger for MBH≳108.5M⊙. This study looks more closely at statistics to see what effect it has on creating, and observing, the MBH–Mbulge correlation. It is possible to show that if galaxy merging statistics can drive the correlation, minor mergers are responsible for causing a convergence to linearity most evident at high masses, whereas major mergers have a central limit convergence that more strongly reduces the scatter. This statistical reasoning is agnostic about galaxy morphology. Therefore, combining statistical prediction (more major mergers ⟹ tighter correlation) with observations (bulges = tightest correlation), would lead one to conclude that more major mergers (throughout an entire merger tree, not just the primary branch) give rise to more prominent bulges. Lastly, with regard to controversial findings that Γ increases with redshift, this study shows why the luminosity function (LF) bias argument, taken correctly at face value, actually strengthens, rather than weakens, the findings. However, correcting for LF bias is unwarranted because the BH mass scale for quasars is bootstrapped to the MBH–σ* correlation in normal galaxies at z = 0, and quasar–quasar comparisons are mostly internally consistent. In Monte-Carlo simulations, high Γ galaxies are indeed present: they are statistical outliers (i.e., “under-merged”) that take longer to converge to linearity via minor mergers. Additional evidence that the galaxies are undermassive at z≳2 for their MBH is that the quasar hosts are very compact for their expected mass.
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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 | 0.006 | 0.048 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".