Studying Binary Formation under Dynamical Friction Using Hill’s Problem
Bibliographic record
Abstract
Abstract Using the equations of motion from Hill’s problem, with added accelerations for different forms of dynamical friction, we provide the (to-date) broadest scale-free study of friction-driven binary formation in gaseous disks and stellar clusters. We focus mainly on binary formation between stellar-mass black holes in active galactic nuclei (AGNs), considering both gas dynamical friction (GDF) from AGN disks and stellar dynamical friction (SDF) from the nuclear star cluster. We first find simple, dimensionless friction coefficients that approximate the effects of standard models for GDF and SDF. We perform extensive simulations of Hill’s problem under such friction, and we present a picture of binary formation through encounters between single stars on nearby orbits, as a function of friction parameter, eccentricity, and inclination. Notably, we find that the local binary formation rate is a linear function of the friction coefficient so long as the friction is weak. Due to the dimensionless nature of our model problem, our findings are generalizable to binary formation at all scales (e.g., intermediate-mass black holes in a star cluster, planetesimals in a gaseous disk).
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".