22 Co-Located, Co-Window Variations of Jet-Base Brightness and Polarization

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: we measure Stokes I (brightness), linear polarization fraction p, and Electric Vector Position Angle (EVPA)—and, when available, circular polarization V—within the same spatial pixel (co-located) and same time window (co-window) near the base of active galactic nucleus (AGN) jets. We then test whether brightness–polarization changes occur simultaneously, are band-insensitive after proper corrections, and track environment strength.

I. One-Sentence Goal

At the jet base (within resolution limits near the core–throat), quantify co-located, co-window variations among I, p, and EVPA (and V when available). After geometric co-registration (including core-shift correction), Faraday-rotation removal, and unified beam/polarization calibration, test for band-insensitive behavior (millimeter–submillimeter–centimeter / optical), significant zero-lag co-occurrence, and monotonic dependence on environment (void → filament/node). If Faraday/beam/pipeline effects or lack of cross-array/team robustness explain the signal, the claim is disfavored.

II. What to Measure

• Co-located, co-window couplings (text tiers): In pre-defined co-located pixels and co-window time grains, record the I–p coupling direction (same / opposite / uncorrelated) with strength (strong / medium / weak), and classify EVPA behavior (steady / slow rotation / rapid flip).
• Zero-lag co-occurrence: With decoupled dual chains and parallel arrays, grade zero-lag peaks and side-lobe/anti-peak contrasts for I↔p and I↔EVPA (strong / medium / weak). Note any significant lag beyond pre-registered thresholds.
• Cross-band non-dispersion: Across mm/submm/cm radio and, when available, optical bands, compare coupling directions and strength rankings. Any λ² or 1/ν-like flips or rescalings indicate medium/chain origins.
• Co-location after core-shift and beam unification: After core-shift correction and common-PSF convolution, verify that co-located curves overlap or agree in sign. If significance appears only before beam unification, classify as beam-driven.
• Environment and geometry layers: Compare coupling strength / zero-lag significance with external convergence κ, external shear γ, distance to filament nodes, void/filament metrics, and the jet–filament angle (enhanced / plateau / uncorrelated). Stratify by optical depth and viewing angle.

III. How to Do It

1. Samples and observing setup:
   • Targets: AGN with strong mm-VLBI polarization capabilities (nearby radio galaxies and blazars), with complementary submm/cm/optical coverage.
   • Arrays and bands: Event Horizon Telescope (EHT), Global Millimeter VLBI Array (GMVA), Very Long Baseline Array (VLBA), Atacama Large Millimeter/submillimeter Array (ALMA), Very Large Array (VLA) at 86–345 GHz and 5–43 GHz; parallel optical polarimetry when feasible.
   • Co-window strategy: Enforce pre-registered simultaneity tolerances (short/medium/long). Where simultaneity is limited, use rapid band switching and flag co-window grade.
2. Imaging and co-registration:
   • Beam unification: Convolve images to a common PSF and resample to a shared pixel grid.
   • Core-shift correction: Register bands via frequency–position relations or cross-correlation of optically thin features.
   • Polarization calibration: Absolute EVPA calibration, D-term leakage and cross-hand phase correction, with playback checks on polarized and unpolarized calibrators.
3. Forward prediction, blinding, arbitration:
   • Environment team (forward): Using the filament–node–void skeleton, κ/γ, jet–filament angle, and activity state, issue prediction cards for I↔p/EVPA coupling direction/strength, zero-lag significance, and cross-band consistency.
   • Measurement teams (independent pipelines): After beam unification + core-shift correction, deliver co-located/co-window curves, zero-lag and side-lobe grades, and non-dispersion checks.
   • Arbitration: Align prediction cards with measurements under pre-registered rules; compute hit / wrong / null rates across bands/arrays/environment bins.
4. Stratification and controls:
   • Optical-depth / viewing-angle stratification: Recompute couplings in opaque / semi-transparent / transparent layers and near-axis / off-axis sightlines.
   • Channel shuffles: Compare de-RM and raw EVPA conventions to isolate Faraday/depolarization effects.
   • Pixel expansion controls: Repeat statistics in jet-base pixels and adjacent downstream pixels to confirm base-specific behavior.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (supporting a path term):
   • Within co-located, co-window pixels, I↔p shows stable same- or opposite-direction coupling with a significant zero-lag peak.
   • After beam unification + core-shift correction, coupling direction and strength ranking are consistent across bands, with no λ²/1/ν flips or rescalings.
   • Environment gradients are monotonic: filament/node, high-κ/high-γ subsets show stronger coupling and zero-lag.
   • Results replicate across independent arrays/pipelines, and prediction-card hit rates exceed chance.
2. Negative controls (against a path term):
   • Coupling changes sign between raw and de-RM frames or follows λ²/1/ν scaling → Faraday/medium driven.
   • Significance appears only without beam unification or core-shift correction → beam/morphology blending.
   • Findings are array- or pipeline-specific, or co-window tolerance violations introduce measurable lags.

V. Systematics and Safeguards (Three Items)

• Faraday rotation and depolarization: can mimic frequency trends in p/EVPA. Safeguard: multi-band de-RM / RM synthesis, sub-band consistency, and report direction agreement before/after de-RM.
• Beam mismatch and core shift: cause morphology–polarization mixing. Safeguard: mandatory common PSF and core-shift correction; recompute with small/large apertures and report scale dependence.
• Polarization calibration and leakage (D-terms): bias p and EVPA. Safeguard: multi-source absolute-angle calibration, cross-hand phase replays, calibration-order swaps, and closure-polarization checks; down-weight unstable epochs.

VI. Execution and Transparency

Pre-register co-location pixels and co-window grains, de-RM conventions, beam/core-shift workflows, text-grade rules for couplings and zero-lag, environment proxies, and control/exclusion policies. Keep hold-out epochs/pixels per environment tier. Enable cross-array/team replication by exchanging visibilities/Stokes images and scripts among EHT/GMVA/VLBA/ALMA/VLA and optical-polarimetry teams. Publicly release prediction cards, coupling and zero-lag grade tables, cross-band non-dispersion summaries, beam/core-shift logs, and key intermediates. This chapter forms a closed loop with Chapters 8 (jet–filament co-alignment), 15 (quasar polarization group alignments—filament synergy), and 7 (co-located scaling near black-hole rings).

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more bands and two or more independent arrays/pipelines, I↔p/EVPA show stable co-located, co-window couplings with significant zero-lag.
   • Cross-band non-dispersion holds after de-RM (no λ²/1/ν flips/rescalings), and effects strengthen in filament/node or high-κ/high-γ subsets.
   • Conclusions are robust after beam/core-shift processing, with prediction-card hits above chance.
2. Refutation (fails):
   • Signals appear only in one array/pipeline or without beam/core-shift and lose co-window status due to lags.
   • After de-RM, coupling reverses or follows dispersive laws.
   • No environmental monotonicity; cross-team replication fails.

22 Co-Located, Co-Window Variations of Jet-Base Brightness and Polarization

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. For general readers: we measure Stokes I (brightness), linear polarization fraction p, and Electric Vector Position Angle (EVPA)—and, when available, circular polarization V—within the same spatial pixel (co-located) and same time window (co-window) near the base of active galactic nucleus (AGN) jets. We then test whether brightness–polarization changes occur simultaneously, are band-insensitive after proper corrections, and track environment strength.

I. One-Sentence Goal

At the jet base (within resolution limits near the core–throat), quantify co-located, co-window variations among I, p, and EVPA (and V when available). After geometric co-registration (including core-shift correction), Faraday-rotation removal, and unified beam/polarization calibration, test for band-insensitive behavior (millimeter–submillimeter–centimeter / optical), significant zero-lag co-occurrence, and monotonic dependence on environment (void → filament/node). If Faraday/beam/pipeline effects or lack of cross-array/team robustness explain the signal, the claim is disfavored.

II. What to Measure

• Co-located, co-window couplings (text tiers): In pre-defined co-located pixels and co-window time grains, record the I–p coupling direction (same / opposite / uncorrelated) with strength (strong / medium / weak), and classify EVPA behavior (steady / slow rotation / rapid flip).
• Zero-lag co-occurrence: With decoupled dual chains and parallel arrays, grade zero-lag peaks and side-lobe/anti-peak contrasts for I↔p and I↔EVPA (strong / medium / weak). Note any significant lag beyond pre-registered thresholds.
• Cross-band non-dispersion: Across mm/submm/cm radio and, when available, optical bands, compare coupling directions and strength rankings. Any λ² or 1/ν-like flips or rescalings indicate medium/chain origins.
• Co-location after core-shift and beam unification: After core-shift correction and common-PSF convolution, verify that co-located curves overlap or agree in sign. If significance appears only before beam unification, classify as beam-driven.
• Environment and geometry layers: Compare coupling strength / zero-lag significance with external convergence κ, external shear γ, distance to filament nodes, void/filament metrics, and the jet–filament angle (enhanced / plateau / uncorrelated). Stratify by optical depth and viewing angle.

III. How to Do It

1. Samples and observing setup:
   • Targets: AGN with strong mm-VLBI polarization capabilities (nearby radio galaxies and blazars), with complementary submm/cm/optical coverage.
   • Arrays and bands: Event Horizon Telescope (EHT), Global Millimeter VLBI Array (GMVA), Very Long Baseline Array (VLBA), Atacama Large Millimeter/submillimeter Array (ALMA), Very Large Array (VLA) at 86–345 GHz and 5–43 GHz; parallel optical polarimetry when feasible.
   • Co-window strategy: Enforce pre-registered simultaneity tolerances (short/medium/long). Where simultaneity is limited, use rapid band switching and flag co-window grade.
2. Imaging and co-registration:
   • Beam unification: Convolve images to a common PSF and resample to a shared pixel grid.
   • Core-shift correction: Register bands via frequency–position relations or cross-correlation of optically thin features.
   • Polarization calibration: Absolute EVPA calibration, D-term leakage and cross-hand phase correction, with playback checks on polarized and unpolarized calibrators.
3. Forward prediction, blinding, arbitration:
   • Environment team (forward): Using the filament–node–void skeleton, κ/γ, jet–filament angle, and activity state, issue prediction cards for I↔p/EVPA coupling direction/strength, zero-lag significance, and cross-band consistency.
   • Measurement teams (independent pipelines): After beam unification + core-shift correction, deliver co-located/co-window curves, zero-lag and side-lobe grades, and non-dispersion checks.
   • Arbitration: Align prediction cards with measurements under pre-registered rules; compute hit / wrong / null rates across bands/arrays/environment bins.
4. Stratification and controls:
   • Optical-depth / viewing-angle stratification: Recompute couplings in opaque / semi-transparent / transparent layers and near-axis / off-axis sightlines.
   • Channel shuffles: Compare de-RM and raw EVPA conventions to isolate Faraday/depolarization effects.
   • Pixel expansion controls: Repeat statistics in jet-base pixels and adjacent downstream pixels to confirm base-specific behavior.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (supporting a path term):
   • Within co-located, co-window pixels, I↔p shows stable same- or opposite-direction coupling with a significant zero-lag peak.
   • After beam unification + core-shift correction, coupling direction and strength ranking are consistent across bands, with no λ²/1/ν flips or rescalings.
   • Environment gradients are monotonic: filament/node, high-κ/high-γ subsets show stronger coupling and zero-lag.
   • Results replicate across independent arrays/pipelines, and prediction-card hit rates exceed chance.
2. Negative controls (against a path term):
   • Coupling changes sign between raw and de-RM frames or follows λ²/1/ν scaling → Faraday/medium driven.
   • Significance appears only without beam unification or core-shift correction → beam/morphology blending.
   • Findings are array- or pipeline-specific, or co-window tolerance violations introduce measurable lags.

V. Systematics and Safeguards (Three Items)

• Faraday rotation and depolarization: can mimic frequency trends in p/EVPA. Safeguard: multi-band de-RM / RM synthesis, sub-band consistency, and report direction agreement before/after de-RM.
• Beam mismatch and core shift: cause morphology–polarization mixing. Safeguard: mandatory common PSF and core-shift correction; recompute with small/large apertures and report scale dependence.
• Polarization calibration and leakage (D-terms): bias p and EVPA. Safeguard: multi-source absolute-angle calibration, cross-hand phase replays, calibration-order swaps, and closure-polarization checks; down-weight unstable epochs.

VI. Execution and Transparency

Pre-register co-location pixels and co-window grains, de-RM conventions, beam/core-shift workflows, text-grade rules for couplings and zero-lag, environment proxies, and control/exclusion policies. Keep hold-out epochs/pixels per environment tier. Enable cross-array/team replication by exchanging visibilities/Stokes images and scripts among EHT/GMVA/VLBA/ALMA/VLA and optical-polarimetry teams. Publicly release prediction cards, coupling and zero-lag grade tables, cross-band non-dispersion summaries, beam/core-shift logs, and key intermediates. This chapter forms a closed loop with Chapters 8 (jet–filament co-alignment), 15 (quasar polarization group alignments—filament synergy), and 7 (co-located scaling near black-hole rings).

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more bands and two or more independent arrays/pipelines, I↔p/EVPA show stable co-located, co-window couplings with significant zero-lag.
   • Cross-band non-dispersion holds after de-RM (no λ²/1/ν flips/rescalings), and effects strengthen in filament/node or high-κ/high-γ subsets.
   • Conclusions are robust after beam/core-shift processing, with prediction-card hits above chance.
2. Refutation (fails):
   • Signals appear only in one array/pipeline or without beam/core-shift and lose co-window status due to lags.
   • After de-RM, coupling reverses or follows dispersive laws.
   • No environmental monotonicity; cross-team replication fails.