Fast frequency-domain effective fly-by waveforms
Bibliographic record
Abstract
Abstract Recently, we developed effective fly-by (EFB) waveforms designed to model the burst of gravitational radiation from highly eccentric binaries. We here present a faster to evaluate frequency domain EFB waveform. The waveform is constructed through the use of asymptotic expansions of hypergeometric functions. Since the waveform is fully analytic, we study the accuracy to which the binary’s parameters can be measured using a Fisher analysis. We find that degeneracies exist among the parameters, such that the waveform is parameterized in terms of the chirp mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">M</mml:mi> </mml:math> and orbital radius of curvature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">P</mml:mi> </mml:math> , instead of the total mass, symmetric mass ratio, and semi-latus rectum of the binary. By computing the Fisher matrix for single bursts from two thousand binary systems, we find that most of the systems will have greater than one hundred percent uncertainty in the chirp mass, luminosity distance, and inclination angle, while roughly half will have less than one hundred percent uncertainty in the orbital radius of curvature, orbital eccentricity, and polarization angle. Further, we repeat this analysis after including additional bursts within the inspiral sequence and find that the uncertainties in the waveform’s parameters can improve by orders of magnitude with a sufficient timing model for the bursts.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".