What the corrected fit shows

Transit supportSUPPORTED (ΔBIC ≥ 10)

Fitted midpoint shift-0.360 h

Model depth23024.9 ± 219.7 ppm

ΔBIC (null − transit)12394.7

The timing-adjusted transit is strongly preferred by ΔBIC = 12394.7. Its fitted midpoint is -0.360 hours from the historical prediction; the model's mid-transit depth is 23024.9 ± 219.7 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 WASP-39 b — The dotted vertical line is the historical archive prediction; the dashed colored line marks the fitted midpoint (-0.360 h). The smooth curve fits timing, radius ratio, impact parameter, and a local linear baseline.

Explicit model comparison

Linear nullχ² 13993.72 / 1570 dof

BIC = 14008.44

Limb-darkened transitχ² 1576.95 / 1567 dof

BIC = 1613.75

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 depth23024.9 +/- 414.4 ppm

Supported / fitted sectors1 / 1

Residual beta range1.89-1.89

The archive prediction was timing-adjusted independently in 1 fitted sector(s) (S51), 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 1.89-1.89). The robust inverse-variance model depth across supported sectors is 23024.9 +/- 414.4 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 WASP-39 b — Independent sector transit fits. Reproduced from the committed public TESS SPOC files.

Sector depth consistency for WASP-39 b — Sector depth consistency. Reproduced from the committed public TESS SPOC files.

Residual RMS time-averaging diagnostic for WASP-39 b — Residual RMS time-averaging diagnostic. Reproduced from the committed public TESS SPOC files.

Published planetary spectrum

Across all 94 observed bins, a weighted-flat spectrum gives chi-square/dof = 1089.6/93 (p = 1.06e-169). Fixed-model comparisons use the 93 bins entirely inside both curves' shared support and fit one vertical offset to each. This diagnostic establishes spectral structure; by itself it is not a molecule-detection or retrieval calculation.

Published transmission spectrum of WASP-39 b — JWST NIRSpec PRISM transmission data from 10.5281/zenodo.6959427. Exact files and checksums are in data/SOURCE.md; numerical tests are in spectrum_statistics.csv.

Atmospheric evidence: detection, limit, or unknown?

The repository's direct calculation shows strong spectral structure and compares two fixed archive products after fitting one vertical offset to each. Detection significances below come from the cited peer-reviewed NIRSpec/G395H retrieval, not from converting the repository diagnostic into sigma.

Source-graded atmospheric evidence — Literature evidence is kept separate from calculations reproduced in this repository.

Species	Status	Evidence	Basis
CO2	reported detection	28.5 sigma	peer-reviewed G395H retrieval
H2O	reported detection	21.5 sigma	peer-reviewed G395H retrieval
SO2	reported evidence	4.8 sigma	peer-reviewed G395H interpretation
CO2 model sensitivity	repository diagnostic	Delta chi-square = 774.4	PRISM full versus remove-CO2 supplied curves; not a retrieval
O2	no evidence	not reported	oxygen-bearing molecules do not imply molecular oxygen

Primary literature source for the quoted significances: Alderson et al. 2023, Nature. Oxygen-bearing molecules are not detections of molecular oxygen (O2) and are not, by themselves, biosignatures.

CO2-sensitive model audit

Strict common support93 / 94 bins

Preprocessing multiverse60 / 60 positive

Multiverse Δχ² range559.6–780.4

Outside 4.1–4.6 μmΔχ² 6.04

The sign survives center versus bin-integrated model sampling, two asymmetric-error rules, factors 1/2/4/8 at every bin origin, every single-bin deletion, and a 20-cell illustrative covariance grid. But removing a 0.5-micron block around the 4.3-micron feature reduces the contrast to 3.19. The supplied-model preference is preprocessing-stable yet strongly localized—not broadband and not a detection sigma.

WASP-39 b supplied-model sensitivity audit across a preprocessing multiverse and covariance grid — Top: strict common-support comparison and per-bin contributions. Bottom: all 60 preprocessing designs and the 20-cell covariance sensitivity grid. Each curve receives the same single fitted vertical offset.

Surface gravity4.26 m s⁻²

Illustrative H2/He scale height983 km

One-scale-height signal421 ppm

Robust spectral modulation3.54 H

Audit summary ↓60-design multiverse ↓Covariance grid ↓Block deletions ↓Bin contributions ↓

The system

Radius	14.34 Earth radii
Mass	89.31 Earth masses
Orbital period	4.055294 days
Transit duration	2.803 hours
Semi-major axis	0.0483 AU
Equilibrium temperature	1166 K
Host and distance	WASP-39 · 213.98 pc
Discovery	2011 · Transit · SuperWASP

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 tess2022112184951-s0051-0000000181949561-0223-s_lc.fits, TESS Sector 51. The PRISM inputs map to exact paths inside Zenodo record 6959427. The source ledger records the archive-object checksum, original-entry hashes, committed-byte hashes, and the line-ending transformation.

Run the five analysis scripts, then python scripts/verify_data_provenance.py and pytest tests/ -v. Continuous integration performs the same provenance check and regenerates the spectral audit before testing.

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.
The full/remove-CO2 test compares two fixed archive curves and does not refit or marginalize chemistry, temperature, clouds, systematics, or limb asymmetry.
The first PRISM bin is excluded because its lower edge falls outside shared model support; extrapolation is prohibited.
The covariance kernels are declared sensitivity tests, not covariances inferred from detector-level residuals.
The scale-height conversion assumes equilibrium temperature and mean molecular weight 2.3.
Published global fits with physical priors, instrument-specific detrending, and simultaneous sectors remain authoritative.

References

Faedi 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 51 used here.
NASA Exoplanet Archive, saved TAP row retrieved 2026-08-15.
JWST Transiting Exoplanet Community ERS Team (2023), Identification of carbon dioxide in an exoplanet atmosphere, doi:10.1038/s41586-022-05269-w.
Alderson et al. (2023), WASP-39b with JWST NIRSpec G395H, doi:10.1038/s41586-022-05591-3.