What the corrected fit shows

Transit supportSUPPORTED (ΔBIC ≥ 10)

Fitted midpoint shift-0.279 h

Model depth5963.4 ± 154.8 ppm

ΔBIC (null − transit)1575.7

The timing-adjusted transit is strongly preferred by ΔBIC = 1575.7. Its fitted midpoint is -0.279 hours from the historical prediction; the model's mid-transit depth is 5963.4 ± 154.8 ppm. The support decision uses ΔBIC ≥ 10; timing-search p-values are not presented as blind-detection probabilities.

Timing-adjusted limb-darkened transit fit for HAT-P-26 b — The dotted vertical line is the historical archive prediction; the dashed colored line marks the fitted midpoint (-0.279 h). The smooth curve fits timing, radius ratio, impact parameter, and a local linear baseline.

Explicit model comparison

Linear nullχ² 3053.49 / 1478 dof

BIC = 3068.09

Limb-darkened transitχ² 1455.87 / 1475 dof

BIC = 1492.37

The null fits a local intercept and slope. The transit adds bounded midpoint, radius-ratio, and impact-parameter freedom while retaining the same baseline terms. Fixed limb darkening and circular geometry make this a diagnostic fit rather than a full system retrieval.

Multi-sector robustness and noise

Supported combined depth5963.4 +/- 164.6 ppm

Supported / fitted sectors1 / 1

Residual beta range1.06-1.06

The archive prediction was timing-adjusted independently in 1 fitted sector(s) (S50), of which 1 meet Delta BIC >= 10. Formal depth errors were inflated by sqrt(max(reduced chi-square, 1)) times the residual time-averaging beta factor (observed range 1.06-1.06). The robust inverse-variance model depth across supported sectors is 5963.4 +/- 164.6 ppm; a sector-to-sector Q test requires at least two supported sectors. These scaled errors address underestimated scatter and short-timescale correlation, but they are not a full Gaussian-process or physical limb-darkened transit fit.

Independent sector transit fits for HAT-P-26 b — Independent sector transit fits. Reproduced from the committed public TESS SPOC files.

Sector depth consistency for HAT-P-26 b — Sector depth consistency. Reproduced from the committed public TESS SPOC files.

Residual RMS time-averaging diagnostic for HAT-P-26 b — Residual RMS time-averaging diagnostic. Reproduced from the committed public TESS SPOC files.

The system

Radius	7.06 Earth radii
Mass	22.25 Earth masses
Orbital period	4.234520 days
Transit duration	2.455 hours
Semi-major axis	0.0475 AU
Equilibrium temperature	1080 K
Host and distance	HAT-P-26 · 141.84 pc
Discovery	2010 · Transit · HATNet

Values are from the exact saved NASA Exoplanet Archive pscomppars row in data/system_parameters.csv.

Data and reproducibility

The observed photometry is the public MAST file tess2022085151738-s0050-0000000420779000-0222-s_lc.fits, TESS Sector 50, collection DOI 10.17909/t9-nmc8-f686. It is stored unmodified. Exact archive URI, URL, retrieval date, and checksum are in data/SOURCE.md.

Run python scripts/analyze_transit.py and python scripts/analyze_multisector.py to regenerate the figures and CSVs, then pytest tests/ -v to check the documented values against the real file.

Limitations

The orbit is circular and the quadratic limb-darkening coefficients are fixed representative values.
The scaled semi-major axis comes from saved composite values whose uncertainties are not propagated.
The midpoint is searched within a bounded window; ΔBIC is used as the support gate.
PDCSAP processing, dilution, stellar variability, timing variations, and covariance can bias the geometry.
Published global fits with physical priors, instrument-specific detrending, and simultaneous sectors remain authoritative.

References

Hartman et al. 2011 — discovery reference listed by the NASA Exoplanet Archive.
Ricker et al. (2015), Transiting Exoplanet Survey Satellite (TESS), doi:10.1117/1.JATIS.1.1.014003.
TESS Team, TESS Light Curves — All Sectors, MAST, doi:10.17909/t9-nmc8-f686; Sector 50 used here.
NASA Exoplanet Archive, saved TAP row retrieved 2026-08-15.