48 Searching for a Common Term in Exoplanet Transit/Occultation Timing Residuals

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. With unified time/frequency standards and source-end calibration, we analyze transit/occultation epochs—mid-times (T_0) and inter-epoch timing (TTV/TDV)—for exoplanets. After removing stellar activity (spots/flares/rotation), atmospheric dispersion (absorption/seeing/color), instrument timing/readout, barycentric corrections, and orbital geometry, we search for a cross-band, cross-instrument, cross-pipeline common timing residual—a nearly non-dispersive, zero-lag constant shift or slow platform reproducible in the same window. If the signal scales dispersively with wavelength, is confined to a single setup, or fails in blinded/held-out tests, the claim is disfavored.

I. One-Sentence Goal

Test whether exoplanet timing residuals contain a frequency-insensitive common term that co-occurs at zero lag across bands/instruments/pipelines and follows predictable geometry/environment patterns.

II. What to Measure

• Common-term index (text grades):
  Using a common bandpass kernel, timescale, and alignment, extract constants and slow slopes from (T_0) residuals and TTV/TDV sequences. Grade strong / medium / weak; advance / delay; stable / unstable on a grid of target (planet × host) × band (optical/NIR/MIR/narrowband) × instrument/station × pipeline (model family/fitting strategy) and tag sign stability.
• Cross-band non-dispersion (narrowband→broadband):
  Require direction and strength of the common term to be insensitive to carrier and band edges across multi-band/narrowband scans. λ or 1/ν flips/scalings indicate atmospheric/device dispersion or stellar chromatic systematics.
• Zero-lag co-occurrence (cross-instrument/pipeline):
  Align (T_0) and TTV/TDV residual series from independent instruments/stations/pipelines to a single external timescale and grade zero-lag peaks and side-lobe contrast. Same-window, synchronized platforms/steps count as supportive.
• Geometry/environment profiles:
  Versus solar/lunar phase, site met (PWV/aerosols/wind/temperature drift), Earth–Sun/Moon tides, geomagnetic Kp/Dst, host rotation phase and activity indices (S-index/photometric variability), label plateau/monotonic/threshold behavior and score forward-prediction hits.
• Ratio robustness and “rigid shift, ratio unchanged”:
  Under unified fits, require depth/duration/slope cross-band ratios to remain stable while absolute (T_0)/TTV show rigid shifts/slow platforms. Drift of parameter ratios across bands downgrades confidence.
• Occultation–phase-curve–Rossiter–McLaughlin (RM) corroboration:
  Check occultations, phase-curve brightness-peak times, and RM sequences for zero-lag co-occurrence with the transit common term; isolation in only one channel downgrades.
• Reproducibility across epochs and targets:
  For the same target over multiple seasons and different targets in similar environment strata, verify sign/order stability. In reference windows away from transits or during quiet stellar phases, the common term should weaken or vanish.

III. How to Do It

1. Observations and facilities:
   Combine space photometry (TESS/PLATO/CHEOPS) with ground follow-up (1–10 m class, multi-site relays). Use simultaneous optical/NIR/MIR with narrowband scans and calibration fields. Acquire high-resolution RV for RM and activity diagnostics (Ca II H&K, Hα). Include same-field comparison stars for differential photometry and color regression.
2. Unified calibration and de-systematics:
   Standardize to TCB/TDB barycentric time; publish BJD/TESS-TIME transforms and timestamp queues. Release per-channel transfer kernels/nonlinearity/drift, map to a common bandpass kernel with band-edge hold-outs. Constrain atmospheric chromaticity via water-vapor radiometers, met stations, and sky brightness, apply GP/PLD/centroid/PSF regressions with inject–recover tests. Remove stellar activity using multi-indicator templates and marginalization.
3. Fitting and pipelines (dual path):
   • Pipeline A (time domain): unified limb darkening/integration/exposure trailing → (T_0)/TTV/TDV extraction → zero-lag index.
   • Pipeline B (frequency/Bayesian): joint sampling of shape–activity–systematics to deliver posteriors for common-term amplitude/shape.
     Publish text-grade strength tables and non-dispersion/zero-lag labels per target × band × instrument × pipeline × window.
4. Stratification and stacking:
   Bin by stellar type (F/G/K/M), activity level, planetary period/eccentricity, observing geometry (solar opposition/elevation), environment (PWV/Kp) and identify plateau/monotonic/threshold patterns. Use method hold-outs (limb-darkening priors, high-pass windows, basis families) to prevent overfitting.
5. Forward prediction, blinding, arbitration:
   The forward team issues prediction cards from geometry/environment layers only; the measurement team reports non-dispersion/zero-lag/amplitude–profile summaries; the arbitration team scores hit / wrong / null by target/band/instrument/pipeline/window.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls:
   • Multi-band/instrument/pipeline detections of same-direction, similar-amplitude smooth constants, robust to band edge/fitting choices.
   • Non-dispersion: no wavelength scaling.
   • Monotonic/plateau/threshold relation with geometry/environment, and prediction cards beat chance.
   • Zero-lag co-occurrence with occultation/phase-curve/RM sequences or physically explainable short lags.
2. Negative controls:
   • Residuals scale with λ/1/ν or correlate with PWV/color/activity templates.
   • Detection confined to one band/instrument/pipeline or fragile to limb-darkening/integration/barycentric settings.
   • Label swaps/time reversals/pipeline swaps/parameter shuffles still “detect” signals—method bias.
   • Stricter atmosphere/activity removal/band-edge hold-outs/timescale audits erase the signal, or readout nonlinearity/exposure trailing/sampling reproduces it.

V. Systematics and Safeguards (Three Items)

• Timescale and barycentric errors: UTC→TDB/BJD transforms and timestamp queues can forge (T_0) biases. Safeguard: two-way clock checks + delay ledgers + inject–recover, with public time audits.
• Atmospheric/chromatic and crowding systematics: PWV/aerosols and centroid drift create false platforms. Safeguard: common bandpass kernel, color regressions, differential photometry with comparison stars, and field hold-outs.
• Stellar-activity coupling: spot crossings/rotation mimic TTVs. Safeguard: multi-indicator activity models, spot-map inject–recover, and activity-posterior marginalization.

VI. Execution and Transparency

Pre-register targets/epochs, bands/instruments, common bandpass/time/barycentric conventions, criteria for non-dispersion/zero-lag/profile shapes, variable lists, positive/negative controls, exclusions, and scoring. Define held-out units (high/low PWV, strong/weak activity, space vs ground, short/long period). Enable cross-team replication by sharing raw light curves/time series, time logs, barycentric/systematics parameters, scripts, and by running down-sampling/noise/kernel-variant/alignment-perturbation/prior scans. Release prediction cards, common-term strength tables, zero-lag/non-dispersion summaries, time/bandpass/atmosphere/activity logs, and key intermediates.

VII. Pass/Fail Criteria

1. Support (passes):
   • In ≥ 2 pipelines, ≥ 2 instruments, ≥ 2 bands and across multiple targets/epochs, recover a non-dispersive, zero-lag common term.
   • The term follows forward-predictable plateau/monotonic/threshold relations with geometry/environment and is robust to bandpass/barycentric/fitting/activity treatments.
   • Arbitration beats chance and replicates in held-out units.
2. Refutation (fails):
   • Results are dominated by dispersion/atmosphere/activity/readout/sampling or fail cross-band/instrument/pipeline/target/epoch replication.
   • High parameter fragility or disappearance/inversion in held-outs.
   • Arbitration near chance, indistinguishable from method/system artifacts.