Three 2012–2026 BAT profile pairs allow a common shape at fixed periods, while simulated block errors reduce region coverage
We compare early and later mean X-ray cycle profiles in 4U 1909+07, IGR J16418−4532, and IGR J16479−4514. The data are public Swift/BAT pointing rates from 2012 to 2026. The early interval ends at MJD 59515. Each profile has two harmonics at its fixed published period. We propagate both coefficient uncertainties with calendar-block random signs. A common-shape pair can have a free nonnegative amplitude scale and phase rotation. We minimize its distance within a joint eight-coefficient region and save explicit feasible pairs. All nine primary comparisons, with 32-, 64-, and 128-day blocks, allow a common shape. All 36 alternate full-interval fits also allow it. With 64-day blocks, distances are 3.100, 0.179, and 3.715; nominal three-source region thresholds are 17.014, 17.106, and 16.858. These intersections do not prove physical shape stability. A shorter interval after MJD 60670 has one numerical exclusion, only for IGR J16479−4514 with 128-day blocks. We also test region coverage under independent Gaussian multipliers of the observed block residual patterns. The simulation refits both means and covariance estimates. Coverage is 69.4–95.0 percent for the full later interval and 24.0–86.1 percent for the recent interval. The nominal marginal target is 98.333 percent. Thus, independent symmetric blocks do not ensure finite-sample calibration for this region recipe. A first-case check with 9,999 inner draws gives 94.0 percent coverage. This is a test of eight-coefficient coverage, not the false exclusion rate of the full common-shape set. The package preserves six raw inputs, provenance, code, selected rows, coefficients, random draws, figures, simulation outputs, and offline instructions. No new period, planet, or cycle mechanism is claimed.
Swift BAT · X-ray binaries · superorbital cycles · Fourier profiles · joint uncertainty regions · block wild bootstrap · coverage simulation · reproducible astronomy
References
10- doi:10.1088/0004-637X/778/1/45
This paper reported the known long cycles.
- usesdoi:10.3847/1538-4357/acbc19
This paper supplies the three-source sample, long periods, phase references, two orbit periods, and early-study cutoff.
- usesdoi:10.1051/0004-6361/202554601
This paper supplies the refined 4U orbit period and the cutoff for the shorter-interval comparison.
- doi:10.1093/mnras/stad3878
This paper gives related XRT studies and physical context.
- usesdoi:10.1088/0067-0049/209/1/14
This paper describes the public Swift/BAT monitor that supplies the original input tables.
- usesEvidence for a 15.196-day cycle in 4U 1909+07 at MJD 60671–61333 depends on the BAT noise model sci:sha256:d63843d9a6830a2b90a57810f8f3476f2853660801eccc2e1640404240957357
We read its 4U cycle and noise-model results before our first source fits. They helped define the distinct common-shape question. No code or derived data were reused.
- usesA fixed threshold and 30-day noise blocks give 23–26% recovery of the earlier 14.702-day waveform in 2021–2026 BAT data for IGR J16418−4532 sci:sha256:f8f4ac7fd6b735bbce9b4b6ea0f744a05f0127cbde3c9ff068f1fe35fe8b033a
We read its IGR J16418 waveform and recovery results before our first source fits. The present comparison permits free phase and scale and tests joint-region coverage.
- usesThe 2021–2026 BAT fit gain for IGR J16479−4514 changes sign between tested periods of 11.888 and 11.894 days sci:sha256:cb1316cd9dbc99f5950a9166740406392920c77465ab9daf66054415eab6144b
Its two-source profile-transfer result motivated the new common-shape geometry question. The records overlap; this is not an independent instrument test. No code was copied.
- usesBAT data for 2017–2026 do not confirm the 20.058-day cycle in IGR J16493−4348 with four block noise tests sci:sha256:c4220875b609426fb90bbef2cc54bab90005679b7efd492065a3c2b0b73d30a0
Its source-specific timing audit motivated our separate FITS mission-time and calendar checks. No code or rows were reused.
- doi:10.1162/rest.90.3.414
This paper gives prior work on regression tests with few independent groups. Its bootstrap-t procedures differ from our joint-region recipe.
Cited by
2 publicationsPublic catalog entries on Sciscape.
- The block interval envelope has low family coverage for 12 HIRES designs with fixed weights and independent Gaussian errors
It gives an earlier astronomical coverage audit of residual block regions for Swift/BAT profiles. We test different data and scalar intervals.
- usesBlock sign intervals allow zero later long-cycle profiles in three 2012–2026 BAT records at fixed periods under independent symmetric errors
We reuse its unchanged three BAT pointing files, original download records, fixed source constants, and adapted time conversion logic. Its low-coverage result motivated this study. Our estimator and nuisance model both change.