43 Cross-Type Stellar Seismology: Testing a Smooth “Floor” Across Oscillation Bands

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 compare stellar classes—solar-like oscillators, red giants, δ Scuti/γ Doradus, white dwarfs, and hot subdwarfs—within their asteroseismic bands to search for a smooth floor. After removing known contributions from instrumentation, sampling, and intrinsic granulation/convection, we test for a cross-type, cross-band, cross-station/pipeline frequency-insensitive common floor. If the floor scales dispersively with frequency, appears in only one setup, or fails to replicate across classes and reobservations, the claim is disfavored.

I. One-Sentence Goal

Determine whether a non-dispersive smooth baseline exists across stellar classes in their seismic bands, co-occurring across bands/stations/pipelines, and reproducible in time—otherwise reject the hypothesis.

II. What to Measure

• Smooth-floor consistency index (text grades):
  After common bandpass/timescale/alignment, extract constant and slow-slope terms from power-spectral density vs frequency and time-domain residuals with discrete modes removed. Grade strong / medium / weak; uplift / depression; stable / unstable on a grid of source (class × sample) × band (photometry/NIR/RV) × station/pipeline × window.
• Cross-band non-dispersion:
  Require insensitivity to carrier and band edge across numerous bands. Dispersive scaling or edge flips imply residual ionosphere/color/device-chain contamination.
• Zero-lag co-occurrence (cross-band/station/pipeline):
  Align residuals to a single timescale and grade zero-lag peaks and side-lobe contrast; same-window, synchronized floor rises/drops count as supportive.
• Cross-type equal-amplitude scaling and profiles:
  Around each class’s ν_max (or principal seismic band), compare floor amplitude versus surface gravity/effective temperature/radius; tag plateau/monotonic/threshold profiles. Equal-amplitude or predictable scaling with similar shapes across classes supports the claim.
• Ratio robustness and “rigid-shift, ratio unchanged”:
  After mode removal, verify that sub-band–sub-band power ratios / polarization ratios / photometry–RV amplitude ratios remain stable while absolute floors show smooth rigid shifts.
• Environment–structure forward predictability:
  Using only line-of-sight environment (sky position, dust column, crowding, satellite straylight background, ground weather/sky brightness) and source structure (convection scales, magnetic activity level, rotation modulation), issue prediction cards (floor sign/magnitude/threshold). Score hit / wrong / null against measurements.
• Reproducibility across epochs and samples:
  For the same star over seasons, different stars within the same class, and different classes with similar environment strata, check sign/order stability; in reference windows far from the main band, the floor should weaken or vanish.

III. How to Do It

• Observing and facilities:
  Space-based photometry plus ground-based radial velocities to obtain high-duty-cycle, months-long time series with minute-level sampling. Record multi-band/photometry/NIR/polarimetry/RV concurrently and run ≥ 2 stations and ≥ 2 independent pipelines (time-domain detrending, spectral modeling, wavelet/empirical-mode) in parallel.
• Unified calibration and de-systematics:
  Publish per-channel transfer kernels, color terms, timestamp queues; map to a common bandpass kernel with band-edge hold-outs. Model granulation/activity with multi-Harvey families and autoregressive backgrounds; perform inject–recover and leave-out–refill tests. Regress straylight/striping/thermal cycles/pixel nonlinearity/crowding and set field hold-outs. Remove rotation/long-period drifts with multi-scale high-pass/cut-window differencing.
• Band/window construction:
  Define the principal seismic band per class (e.g., ν_max± several mode widths for solar-like; low-frequency for red giants; mid/high vs low for δ Sct/γ Dor; low-temperature mode bands for white dwarfs) and adjacent sidebands. Publish floor-consistency and zero-lag indices across class × band × station/pipeline × window.
• Stratification and stacking:
  Bin by log g/Teff/activity index/dust column/sky field/crowding, and tag plateau/monotonic/threshold behavior. Use method hold-outs (alternate high-pass lengths, windows, and background templates) to suppress overfitting.
• Forward prediction, blinding, arbitration:
  The forward team issues prediction cards from environment/structure layers only; the measurement team independently reports floor/zero-lag summaries; the arbitration team reconciles them and scores hit / wrong / null by class/band/station/pipeline/window.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (support a smooth common floor):
   • Within the same window, multi-band/station/pipeline data show same-direction, similar-amplitude smooth floors, robust to band edge/high-pass/window/template choices.
   • Non-dispersion: floors do not scale with frequency.
   • Floors vary monotonically/plateau with environment/structure and show threshold boosts in high dust/background/strong activity or specific convection–magnetic states.
   • Prediction-card hit rates exceed chance and replicate in held-out stars/epochs.
2. Negative controls (argue against a common floor):
   • Floors follow dispersive scaling or correlate with color/ionosphere/straylight/readout noise.
   • Significance confined to one band/pipeline/station/class, or fragile to bandpass/alignment/window/high-pass/template choices.
   • Label swaps/time reversal/method swaps/parameter shuffles still “detect” floors—selection/method bias.
   • Signals vanish under stricter background modeling, band-edge hold-outs, crowding controls, or can be reproduced by underfit granulation/spectral leakage/thermal drift.

V. Systematics and Safeguards (Three Items)

• Granulation-template misplacement: underfitting backgrounds forge floors. Safeguard: template-family ensembles, cross-validation, and inject–recover bias checks.
• Sampling window and spectral leakage: duty-cycle changes and sector switches create 1/f tails and side-lobe filling. Safeguard: multi-window corrections, cross-mission stitching, ground fill, and simulation + hold-out robustness.
• Crowding and straylight: neighbor flux and attitude-dependent straylight project low-frequency floors. Safeguard: difference imaging/neighbor templates/attitude-thermal regressions with field hold-outs.

VI. Execution and Transparency

Pre-register sample/class quotas, sampling/bands, common bandpass/timescale settings, criteria for non-dispersion/zero-lag/profile shapes, environment/structure variables, positive/negative controls, exclusions, and arbitration. Reserve held-out windows (quiet/active/sidebands). Enable cross-team replication via raw light curves/RV time series, timestamp logs, calibration/color files, and scripts; run down-sampling/noise/kernel-variant/alignment-perturbation/template-family swaps. Publicly release prediction cards, floor-consistency tables, zero-lag/non-dispersion summaries, bandpass/color/straylight/sampling logs, and key intermediates.

VII. Pass/Fail Criteria

1. Support (passes):
   • In ≥ 2 pipelines, ≥ 2 stations, ≥ 2 bands and across multiple classes/epochs, recover a non-dispersive, zero-lag smooth floor.
   • The floor shows monotonic/plateau trends with environment and source structure, and remains robust to bandpass/alignment/window/high-pass/template/crowding choices.
   • Arbitration exceeds chance and reproduces in held-out units.
2. Refutation (fails):
   • Floors are dominated by dispersion/color/sampling/crowding or underfit granulation, or fail replication across band/station/pipeline/class/epoch.
   • High parameter fragility or disappearance/inversion in held-out sets.
   • Arbitration near chance—indistinguishable from system/method artifacts.