The Photometric Amplitude and Mass Ratio Distributions of Contact Binary Stars
Bibliographic record
Abstract
The distribution of the light variation amplitudes A ( a ), in addition to determining the number of undiscovered contact binary systems falling below photometric detection thresholds and thus lost to statistics, can serve as a tool in determination of the mass ratio distribution Q ( q ), which is very important for understanding of the evolution of contact binaries. Calculations of the expected A ( a ) show that it tends to converge to a mass ratio dependent constant value for a → 0. Strong dependence of A ( a ) on Q ( q ) can be used to determine the latter distribution, but the technique is limited by the presence of unresolved visual companions and by blending in crowded areas of the sky. The bright-star sample to 7.5 mag is too small for an application of the technique, while the Baade's window sample from the OGLE project may suffer stronger blending; thus the present results are preliminary and illustrative only. Estimates based on the Baade's window data from the OGLE project, for amplitudes a > 0.3 mag, where the statistics appear to be complete allowing determination of Q ( q ) over 0.12 ≤ q ≤ 1, suggest a steep increase of Q ( q ) with q → 0. The mass ratio distribution can be approximated by a power law, either Q a ( q ) ∝ (1 - q ) a 1 with a 1 = 6 ± 2 or Q b ( q ) ∝ q b 1 with b 1 = -2 ± 0.5, with a slight preference for the former form. While both forms would predict very large numbers of small mass ratio systems, these predictions must be modified by the theoretically expected cutoff caused by a tidal instability at q min ≃ 0.07–0.1. A maximum in Q ( q ), due to the interplay of a steep power-law increase in Q ( q ) for q → 0 and of the cutoff at q min , is expected to be mapped into a local maximum in A ( a ) around a ≃ 0.2–0.25 mag. When better statistics of the amplitudes are available, the location of this maximum will shed light on the currently poorly known value of q min . The correction factor linking the apparent, inclination-uncorrected frequency of W UMa–type systems to the true spatial frequency remains poorly constrained at about 1.5 to 2 times.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".