Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory
Bibliographic record
Abstract
We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of nonspinning moderately eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasicircular NR waveforms. The use of circular merger waveforms is possible because binaries with moderate eccentricity circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q={m}_{1}/{m}_{2}=3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting $\ensuremath{\approx}20$ cycles before the merger with eccentricities ${e}_{\mathrm{ref}}\ensuremath{\le}0.1$ and mass ratios $q\ensuremath{\le}3$, where ${e}_{\mathrm{ref}}$ is the eccentricity $\ensuremath{\approx}7$ cycles before the merger. The NR waveforms are long enough that they start below 30 Hz (10 Hz) for BBH systems with total mass $M\ensuremath{\ge}80\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ ($230\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$). We find that, for the sensitivity of advanced LIGO at the time of its first observing run, the eccentric model has a faithfulness with NR of over 97% for systems with total mass $M\ensuremath{\ge}85{M}_{\ensuremath{\bigodot}}$ across the parameter space (${e}_{\mathrm{ref}}\ensuremath{\le}0.1$, $q\ensuremath{\le}3$). For systems with total mass $M\ensuremath{\ge}70{M}_{\ensuremath{\bigodot}}$, the faithfulness is over 97% for ${e}_{\mathrm{ref}}\ensuremath{\lesssim}0.05$ and $q\ensuremath{\le}3$. The NR waveforms and the Mathematica code for the model are publicly available.
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".