What the corrected fit shows

Transit supportNOT BIC-SUPPORTED

Fitted midpoint shift+3.478 h

Model depth10830.9 ± 2770.3 ppm

ΔBIC (null − transit)-4.8

The best transit-shaped profile is not supported over the local linear null (ΔBIC = -4.8). Its fitted depth and timing are therefore exploratory optimizer outputs, not a transit measurement. The support decision uses ΔBIC ≥ 10; timing-search p-values are not presented as blind-detection probabilities.

Timing-adjusted limb-darkened transit fit for Kepler-51 b — The dotted vertical line is the historical archive prediction; the dashed colored line marks the fitted midpoint (+3.478 h). The smooth curve fits timing, radius ratio, impact parameter, and a local linear baseline.

Explicit model comparison

Linear nullχ² 954.33 / 1036 dof

BIC = 968.22

Limb-darkened transitχ² 938.31 / 1033 dof

BIC = 973.04

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 depthNot reported

Supported / fitted sectors0 / 1

Residual beta range1.04-1.04

The archive prediction was timing-adjusted independently in 1 fitted sector(s) (S14), of which 0 meet Delta BIC >= 10 from 2 committed files; 1 lacked adequate fixed-window sampling. Formal depth errors were inflated by sqrt(max(reduced chi-square, 1)) times the residual time-averaging beta factor (observed range 1.04-1.04). No fitted sector reaches the Delta BIC >= 10 support threshold, so no combined transit depth or sector-consistency claim is reported. 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 Kepler-51 b — Independent sector transit fits. Reproduced from the committed public TESS SPOC files.

Sector depth consistency for Kepler-51 b — Sector depth consistency. Reproduced from the committed public TESS SPOC files.

Residual RMS time-averaging diagnostic for Kepler-51 b — Residual RMS time-averaging diagnostic. Reproduced from the committed public TESS SPOC files.

The system

Radius	7.10 Earth radii
Mass	2.10 Earth masses
Orbital period	45.154000 days
Transit duration	5.797 hours
Semi-major axis	0.2514 AU
Equilibrium temperature	543 K
Host and distance	Kepler-51 · 783.83 pc
Discovery	2012 · Transit · Kepler

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 tess2019198215352-s0014-0000000027846348-0150-s_lc.fits, TESS Sector 14, 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

Steffen et al. 2013 — 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 14 used here.
NASA Exoplanet Archive, saved TAP row retrieved 2026-08-15.