A sine model gave smaller later timing errors than a linear model for 23 of 26 selected Kepler planet pairs
We tested later Kepler transit time predictions from a sine model with a period set by early orbital fits. We used Holczer et al. (2016) timing measurements and a frozen NASA KOI table. A fixed split at BJD 2456000 and fixed sample rules left 73 adjacent confirmed planet pairs near first-order orbital resonances. An early selection score of at least 10 for either member selected 26 pairs at 25 stars. These pairs contain 51 distinct planets and 1363 distinct later measurements. All model coefficients and the sine period use early timing values. The sine model gave smaller later weighted timing errors than a linear model for 23 of 26 selected pairs. The median pair error ratio was 0.811. A star bootstrap gave a descriptive 95 percent interval of 0.720 to 0.866. Both members improved in 20 pairs. The sine model also gave smaller errors than a quadratic model in 24 pairs, with a median ratio of 0.717. Across all 73 eligible pairs, the median sine-to-linear ratio was 0.988. Seven planned changes to the sample or fit rules gave selected-sample median ratios from 0.801 to 0.832. Parser, solver, time conversion, test-value isolation, simulation, and repeat checks are preserved. The contribution is a reproducible prediction benchmark with complete inputs, pair decisions, coefficients, predictions, controls, and figures. Full-record source templates, quality flags, and archive status limit the test. It does not establish a new planet or accuracy beyond the tested later Kepler dates.
Kepler · transit timing · superperiod · orbital resonance · prediction · model selection · reproducible benchmark
References
7- usesdoi:10.3847/0067-0049/225/1/9
Holczer et al. (2016) supply the original Kepler timing data, errors, flags, and catalog periods. We downloaded Tables 2 and 3 from CDS J/ApJS/225/9.
- usesdoi:10.26133/NEA4
The NASA cumulative KOI table supplies the frozen star identifiers, names, confirmed status, and period order.
- usesLater quadratic timing errors were larger than linear errors for 16 of 28 selected Kepler objects with a 70/30 split sci:sha256:da64194e286627a311d45cba907c643cfba74dd47966c96b347c71fb747f32c5
We use its frozen NASA KOI snapshot and its original source hashes. It also provides a related early-to-later linear and quadratic timing benchmark. The new pair analysis and code are independent.
- usesdoi:10.1088/0004-637X/761/2/122
Lithwick, Xie, and Wu (2012) give the approximate superperiod timing model near first-order resonance and its physical limits.
- doi:10.1088/0004-637X/787/1/80
Hadden and Lithwick (2014) apply the near-resonance sine timing framework to Kepler planets.
- doi:10.3847/1538-4365/aa9f2b
Ofir et al. (2018) establish prior use of sine models for transit timing detection. The sine model is not a new method here.
- doi:10.1093/mnras/staf334
Kaye and Aigrain (2025) compare Kepler and K2 transit ephemerides with later TESS observations. Later timing checks have prior use.
Cited by
6 publicationsPublic catalog entries on Sciscape.
- usesExact opposite phases gave almost the same mean timing forecast error as separate phases in 26 selected Kepler pairs
We reuse its frozen input files, unchanged MIT parser, early period fits, eligibility rules, and selection rule. We reproduce its main separate-model scores before the new joint comparison.
- usesCompanion updates gave a mean forecast error ratio of 0.981 in 26 selected Kepler pairs with a fixed wave ratio
We use its unchanged parser, sample rules, early period estimates, and separate early models through the direct parent package.
- Frequency uncertainty left 4 of 12 first TESS group means outside 95 percent intervals from one timing wave
This earlier SCI work tests wave forecasts within Kepler data.
- usesNo added circular chopping term passed early selection in 146 Kepler timing records
We reuse its frozen inputs, sample rules, and MIT benchmark code. We reproduce its primary counts and score summaries.
- usesA local frequency closure rule changed later timing errors by less than 1% in 22 of 26 selected Kepler pairs
We reuse its verified input bytes, sample rules, early selection, and MIT analysis code. The new work tests local frequency closure and a free-frequency control against its fixed-frequency predictions. We also reproduce its eligible sample, selected sample, frequencies and scores.
- Fixed 1102-day timing waves reduce forecast errors for TOI-270 c and d in TESS sectors 97 and 98
A prior test compares fixed-period timing waves with clocks for selected Kepler pairs. The present code and TOI-270 measurements are independent.