The Mass Density of Merging Binary Black Holes over Cosmic Time
Bibliographic record
Abstract
Abstract The connection between the binary black hole (BBH) mergers observed by LIGO-Virgo-KAGRA and their stellar progenitors remains uncertain. Specifically, the fraction ϵ of stellar mass that ends up in BBH mergers and the delay time τ between star formation and merger carry information about the astrophysical processes that produce merging BBHs. We model the merger rate in terms of cosmic star formation, coupled with a metallicity-dependent efficiency ϵ and a distribution of delay times τ, and infer these parameters with data from the Third Gravitational-Wave Transient Catalog. The progenitors to merging BBHs preferentially form in low-metallicity environments with a low-metallicity efficiency of log 10 ϵ < Z t = − 3.99 − 0.87 + 0.68 and a high-metallicity efficiency of log 10 ϵ < Z t = − 4.60 − 0.34 + 0.30 at 90% credibility. The data also prefer short delay times. For a power-law distribution p(τ) ∝ τ α , we find τ min < 1.9 Gyr and α < −1.32 at 90% credibility. Our model allows us to extrapolate the mass density in BBHs to high redshifts. We cumulatively integrate our density rate over time to get the total density of merging stellar-mass BBHs as a function of redshift. Today, BBH mergers are only ∼0.01% of the total stellar-mass density created by >10 M ⊙ progenitors. However, because massive stars are short lived, there may be more mass in merging BBHs than in living massive stars as early as ∼2.5 Gyr ago. We also compare to the mass in supermassive black holes, finding that the densities were comparable ∼12.5 Gyr ago, but their densities quickly increased to ∼75 times the density in merging stellar-mass BBHs by z ∼ 1.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".