Biswajit Jana · Time-domain research

WASP-12 b · orbital timing dossier · version 2.0

Reproducing a decaying orbit.

A source-audited recalculation of one of exoplanet science’s clearest orbital-decay cases—using 379 public transit times, an independent transit-and-occultation model test, and six homogeneous TESS sectors.

Transit times379
Timing baseline14.1 yr
Period derivative−31.29 ms yr⁻¹
Scaled uncertainty±1.09 ms yr⁻¹
Decay timescale3.01 Myr
Artistic concept of the ultra-hot Jupiter WASP-12 b close to its host star
Artistic concept—not an observation and not to scale. The prolate silhouette visualizes the tidal deformation inferred from phase-curve studies; the dark, intensely heated atmosphere and low-reflectivity treatment follow the measured extreme irradiation and low dayside albedo. Colors, cloud structure and viewing geometry are interpretive. Visual basis and provenance.
01 / Long baseline

The curvature is large, coherent, and reproducible.

A weighted quadratic ephemeris fitted to the complete 379-row VizieR compilation gives Ṗ = −31.29 ± 0.76 ms yr⁻¹ formally. The quadratic model improves BIC by 1687 relative to a linear ephemeris.

The fit has χ²/dof = 2.04, so the public headline uses a scatter-scaled uncertainty of ±1.09 ms yr⁻¹. Error inflation is not a covariance model, but it prevents the diagonal formal error from being presented as the whole uncertainty story.

Long-baseline WASP-12 b timing curvature and independent TESS timing check
Figure 1. Top: 379 public transit timings relative to the best linear ephemeris, with the fitted quadratic curvature. Bottom: the separate six-sector TESS-only experiment. The panels answer different questions and are not pooled.
02 / Model challenge

Decay outperforms a precession-like timing pattern.

Transit curvature alone is not the decisive physical discriminator. Occultations should shift oppositely under apsidal precession, so the older 158-event transit-and-occultation set is retained for an explicit alternative-model check.

TestResultInterpretation
Quadratic vs linearΔBIC = 202.52Strong curvature in the Yee et al. set
Quadratic vs apsidal proxyΔBIC = 20.16Quadratic decay preferred
Proxy search window5–100 yrBest fit approaches the upper boundary; proxy period is not interpreted
Published physical comparisonΔBIC = 22.3Yee et al. also preferred decay and used radial velocities to reject a Rømer explanation

The proxy solves an opposing-sign sinusoid over a declared precession-period interval. It is useful as a transparent falsification test, not as a replacement for a small-eccentricity physical posterior.

03 / Influence

No major literature source creates the result.

Deleting each source group represented by at least five measurements leaves Ṗ between −31.93 and −30.35 ms yr⁻¹. Every refit still gives ΔBIC > 1293 in favor of quadratic curvature.

Leave-one-literature-source-out period derivative estimates for WASP-12 b
Figure 2. Source-group deletion analysis. Horizontal bars are scatter-scaled errors; the vertical line and band show the all-source estimate. This tests group leverage, not unpublished shared covariance.
04 / Independent TESS check

Six sectors support the trend, but not by themselves.

All six target-specific 120-second SPOC sectors produce supported transit fits. The 119 event mid-times give a conditional Ṗ = −22.6 ± 21.5 ms yr⁻¹, while BIC still prefers the linear TESS-only ephemeris by 3.68. That result is correctly treated as insufficient.

The independent TESS subset is consistent with the established decay scale but does not detect curvature on its own. Consistency is not confirmation when the uncertainty is this broad.

Six independently fitted TESS transit sectors for WASP-12 b
Figure 3. Timing-adjusted sector transit fits.
Time-averaging noise diagnostic for six WASP-12 b TESS sectors
Figure 4. Residual RMS diagnostic used to inflate formal depth errors.
Six-sector TESS depth consistency for WASP-12 b
Figure 5. Combined depth 15,348.3 ± 36.6 ppm; Cochran Q = 10.72 for 5 degrees of freedom (p = 0.057). The marginal tension is not promoted to an atmospheric-variability claim.
05 / Analysis chain

A calculation designed to be inspected.

01

Archive

Version the verbatim VizieR response and six unmodified TESS FITS products.

02

Verify

Require every scientific input to match its documented SHA-256 digest.

03

Condition

Center event coordinates before weighted fits to control polynomial conditioning.

04

Compare

Evaluate linear, quadratic and opposing-sign sinusoidal timing models with BIC.

05

Stress-test

Delete source groups and report both formal and scatter-scaled uncertainty.

06

Separate

Keep new TESS photometry distinct from the literature timing reproduction.

06 / Open materials

Inputs, outputs, and provenance are public.

pip install -r requirements.txt
python scripts/analyze_transit.py
python scripts/analyze_multisector.py
python scripts/analyze_orbital_decay.py
pytest tests/ -v
07 / Boundaries

What the reproduction does not prove.

  • The 379 timing errors are treated as diagonal; source-group deletion cannot reconstruct shared reduction covariance.
  • Scatter scaling is a conservative diagnostic, not a physical red-noise likelihood.
  • The apsidal sinusoid is a bounded proxy, not an eccentricity measurement or a full posterior reproduction.
  • The TESS event fits share sector-level shapes and detrending systematics.
  • Fixed limb darkening, circular geometry and saved composite system parameters limit the transit fits.
  • Q′★ depends on the tidal convention and adopted stellar/planet parameters.
  • The analysis reproduces public evidence; it does not claim discovery of orbital decay.
  • A future departure from constant Ṗ would require a new dynamical model and longer monitoring.
08 / Primary sources

Research context.

  1. Yee et al. (2020), The Orbit of WASP-12b Is Decaying, doi:10.3847/2041-8213/ab5c16.
  2. Wong et al. (2022), TESS Revisits WASP-12, doi:10.3847/1538-3881/ac5680.
  3. Leonardi et al. (2024), TASTE V. A new ground-based investigation, doi:10.1051/0004-6361/202348363.
  4. Akinsanmi et al. (2024), The tidal deformation and atmosphere of WASP-12b from its phase curve, arXiv:2402.10486.
  5. TESS Team, TESS Light Curves — All Sectors, MAST, doi:10.17909/t9-nmc8-f686.
  6. Leonardi et al. timing catalogue, VizieR, doi:10.26093/cds/vizier.36860084.