21 Excess Suppression (“Ablation”) of Saddle Images in Strong Gravitational Lenses: A Statistical Test

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. For general readers: in four-image strong lenses (including fold and cusp geometries), we evaluate whether saddle-point images are systematically dimmer than minimum images even after careful modeling and removal of known effects. We then test if this “saddle ablation” is band-insensitive, time-stable, geometry-ordered, and environment-linked.

I. One-Sentence Goal

Build a publication-grade statistic for the excess rate and strength of saddle-image “ablation” relative to minima in four-image lenses. After aligning macro models and geometry, applying time-delay corrections, and stripping out dust/plasma/microlensing and source-side effects, test whether ablation is non-dispersive (radio—mid-IR—narrow-line agree), time-stable (multi-epoch same-sign), monotonic with external convergence/environment grade (void → filament/node), and robust to model families and pipelines. If microlensing, extinction/scattering, or macro-model degeneracies explain the pattern—or robustness is lacking—the claim is disfavored.

II. What to Measure

• Ablation strength and excess rate (text tiers):
  With image positions fitted to high precision, define residual magnification offsets and relative-flux thresholds. For each saddle image, grade ablation as significant / moderate / mild and compute the excess rate of ablation relative to minima.
• Non-dispersion across bands:
  Compare direction and rank order of ablation in radio/VLBI, mid-infrared, and narrow-line channels (for example, [O III] or mm CO narrow lines). Any λ² or 1/ν-like flips/scalings indicate plasma/scattering origins.
• Time stability:
  After time-delay alignment of epochs, check whether ablation direction and grade persist. Long-timescale drifts—not short microlensing flickers—strengthen the case.
• Geometry and parity stratification:
  Bin by parity (saddle/minimum), distance to critical curve, magnification level, and fold/cusp geometry. Test for monotonic gradients (closer to the critical curve and more highly magnified → stronger ablation).
• Environment linkage:
  Relate ablation excess to external convergence κ_ext, external shear γ_ext, distance to nodes, and void/filament metrics, graded enhanced / plateau / uncorrelated. Compare lenses in groups/clusters/filaments vs in voids.

III. How to Do It

1. Samples and baselines:
   • Select quad lenses with radio-bright (VLBI-resolved), mid-IR bright, and narrow-line subsets.
   • Build macro-model families (elliptical potentials / power-law / free-form + external shear) using positions first; hold out fluxes for validation only.
2. Parity and geometry labels:
   From the macro-model Fermat-surface Hessian, tag image parity, record critical distance and local magnification, and form the (parity–distance–magnification) stratification.
3. Band and source-region choices:
   • Minimize microlensing: emphasize radio/mid-IR/narrow-line (large source regions). Use optical/NIR continuum and broad lines only as comparisons.
   • Remove dust/scattering: apply color laws / λ² broadening and RM/DM indicators to filter dusty/scattered sightlines.
4. Timing and pipelines:
   • Align time delays from monitored light curves or cross-correlation before comparing fluxes.
   • Independent reprocessing: multiple teams use independent modeling and photometry pipelines (no shared parameters/code) to re-grade ablation.
5. Forward prediction, blinding, arbitration:
   • Environment team (forward): using only κ_ext, γ_ext, void–filament–node skeletons and geometric labels, issue prediction cards for ablation excess, strength tier, and geometric gradient (closer → stronger).
   • Measurement team: deliver banded, epoch-aligned ablation grades and excess rates plus non-dispersion and time-stability verdicts.
   • Arbitration: match predictions to results via pre-registered rules; compute hit / wrong / null rates with stratified statistics.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls:
   • In radio/mid-IR/narrow-line, saddles show significantly excess ablation over minima, increasing monotonically with critical proximity and magnification.
   • Multi-epoch direction stability and cross-band non-dispersion hold. In high κ_ext / node environments, the excess rate is significantly higher than in voids, matching prediction-card ordering.
   • Conclusions agree across institutions/pipelines and macro-model families.
2. Negative controls:
   • Strong ablation in optical/NIR that vanishes in radio/mid-IR/narrow-line while following color laws/time flicker → microlensing/dust.
   • Ablation amplitudes that scale with λ²/1/ν or co-vary with RM/scattering → plasma scattering.
   • Signals confined to one model/pipeline/institution or sensitive to minor macro tweaks → modeling/pipeline bias.

V. Systematics and Safeguards (Three Items)

• Macro-model degeneracies (mass sheet/source-position transformations): can mis-assign flux offsets. Safeguard: position-first fitting + model-family ensembles; report model-dependence strata; use surface-brightness constraints from arc/ring systems.
• Time delays and intrinsic variability: misalignment fakes ablation. Safeguard: robust delay alignment with hold-out epochs; down-weight fast variables.
• Aperture/resolution and channel mismatch: blending or aperture mismatch biases fluxes. Safeguard: unified photometric apertures, PSF deconvolution, and VLBI baselines; report resolution dependence.

VI. Execution and Transparency

Pre-register sample and geometric bins, model families, ablation thresholds and text-grade rules, non-dispersion/time-stability criteria, and control/exclusion policies. Maintain hold-out lenses and epochs per environment bin. Arrange cross-team replication with exchanged positions/photometry tables and modeling scripts, plus down-sampling/noise-injection robustness tests. Publicly release prediction cards, ablation-excess tables, non-dispersion/time-stability summaries, model-dependence reports, and key intermediates. This chapter closes a loop with Chapters 9 (smooth-field account of flux-ratio anomalies), 2 (environment-forward potential terms), and 27 (path-redshift tomography).

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more bands (including radio/mid-IR/narrow-line) and two or more institutions, observe excess saddle ablation that rises monotonically with critical distance / magnification / environment grade.
   • Non-dispersion and time stability hold, and environment-forward hit rates for strength/order are significantly above chance.
   • Results are robust to model family and pipeline choices; negative controls cannot reproduce the full signature set.
2. Refutation (fails):
   • Excess is near chance or appears only in optical / one pipeline.
   • Ablation flips with frequency or follows dispersive laws, or tracks time flicker.
   • No environmental monotonicity, cross-team replication fails, or findings are highly model-sensitive.