Stochastic period fluctuation as a null hypothesis for RR Lyrae binary candidates identified from O−C timing

Searches for binary companions to RR Lyrae stars using the light-travel-time effect (LTTE) in observed-minus-calculated (O−C) pulsation timing have produced candidate lists numbering in the dozens, the largest containing 87 objects from OGLE bulge photometry. Independently, it is established that RR Lyrae pulsation periods undergo stochastic cycle-to-cycle and random-walk fluctuation generating O−C excursions of comparable amplitude and timescale to the predicted orbital signal, and individual candidates have been withdrawn on exactly these grounds. What has not been done is to compare the two hypotheses on the same data under the same likelihood, for a published candidate sample: the statistical model family used for RR Lyrae O−C contains no periodic member, and the candidate searches fit LTTE orbits under a chi-squared likelihood with independent errors and no correlated-noise term. This note supplies that comparison. I extend the Koen (2006) covariance framework with an LTTE mean function, correct two misprints in the published statement of the underlying model, validate the implementation by Monte Carlo and by parameter recovery, and apply it in three ways. First, a parametric bootstrap under each candidate's own fitted noise model, on its own cadence, selects a companion for a companion-free star in 0%–15% of draws under AIC, counting only spurious orbits that fall inside the ranges the published sample spans; on a synthetic grid the rate reaches 25% in one cell of 20 (95 per cent interval 14%–40%), in one part of the grid; the 6 cells whose noise parameters bracket the real candidates give 0%–25%, overlapping the per-star result but running higher. Second, the reported trimodality of the published companion-mass distribution is better supported than the discovery paper established and less securely than a component count alone would suggest. The count does not settle it: three Gaussian components beat two Gaussian components, but a two-population model with one skewed component fits these data equally well (ΔBIC 0.86) and reproduces a three-component preference 14% of the time. What does discriminate is the narrowness of the fitted components, which two-population models fitted to these data reproduce rarely (p = 0.58% against the strongest of them, over 20000 draws), though that statistic measures structure rather than number and was the third tried. What remains open is whether the lowest mode is a sub-stellar population or an accumulation of the false positives located above. Third, for the five candidates whose light curves the discovery authors published, an independent reimplementation of their extraction reproduces their orbital periods to a median of 0.3 per cent and their mass functions to a median of 3.4 per cent, confirming the pipeline; under the noise-aware comparison 1 of the five is preferred as pure stochastic period change with no companion on both AIC and BIC, 2 are split between the criteria and 2 prefer the companion on both. For 3 of the five the preferred model's pseudo-residuals are not normal while noise-only members of the family pass; on 07640 that reverses what the bootstrap implies, leaving no confident statement about a companion from O−C alone. I do not claim that these candidates are spurious. I claim that the evidence for them had not been tested against the relevant null, that the test is inexpensive, and that applying it changes the picture for most of what it is applied to — in one place by withdrawing confidence from a candidate, in another by putting a published claim on evidence it never had while showing that the evidence still does not settle it. The deposited archive contains the code and the JSON outputs from which every number in the manuscript's tables and every statistic quoted in its text is read by the manuscript builder rather than transcribed, together with the extracted O−C curves and a README giving the exact invocation that produced each output.