8 Axial “Perforation” in Active Galactic Nucleus Jets and Co-Alignment with Cosmic Filament Orientation

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and keeps the structure fixed. At first mention, we expand abbreviations for general readers (for example, Active Galactic Nucleus (AGN), Very Long Baseline Interferometry (VLBI), Rotation Measure (RM)).

I. One-Sentence Goal

Test two linked claims in resolved samples of Active Galactic Nucleus (AGN) jets using the local orientation of the cosmic-filament skeleton. First, ask whether the jet axis and the local filament co-align statistically. Second, probe whether a narrow axial “perforation corridor” exists along the jet axis in which path-integrated quantities—such as Rotation Measure depth and gradient, emission measure or dispersion measure, and absorbing column density—depress or reorganize in a predictable way. If co-alignment plus perforation recur in the same normalized angular sector, strengthen monotonically with environment class (void → filament/node), and remain broadly band-insensitive, the result supports a path contribution in Energy Filament Theory (EFT). Otherwise, the claim is disfavored.

II. What to Measure

1. Orientation co-alignment: Measure the absolute position-angle difference, |ΔPA|, between the jet axis and the cosmic-filament principal axis at the target’s sky location. Compare the fractions of co-aligned (small |ΔPA|) and misaligned (large |ΔPA|) systems across environment grades.
2. Axial perforation corridor indicators: Define a narrow sector about the jet axis and a quadrature control sector orthogonal to it; compare:
   • Rotation Measure (RM) depth and gradient: look for valleys and enhanced smoothness along the axis.
   • Emission/dispersion measures: quantify depressions in integrated tracers accessible at radio, millimeter, or optical bands.
   • Absorbing column density: identify axial dimples and their angular width using H I, Na D, or soft-X-ray absorption.
3. Multi-probe consistency: In the same object, check whether axial-versus-control differences agree in radio polarization, total intensity, optical/UV absorption, and X-ray absorption.
4. Environment monotonicity and frequency independence: Expect stronger and narrower signals in filament/node corridors and weaker ones in voids. Verify that the sign and relative amplitude do not flip or rescale systematically with observing band.

III. How to Do It

1. Samples and environment templates:
   Build a target set of AGN (radio galaxies/quasars) with clearly resolved one- or two-sided jets and polarization-quality maps across 86–1500 MHz (low-frequency morphology/polarization) and 1–100 GHz (high-frequency polarization/cores). For each target, derive an environment skeleton from public surveys: filament principal axis, distance to nodes, and local-density grade. For every target, select (a) a nearby control with similar redshift/brightness but clear misalignment between jet and filament axes, and (b) additional void-environment controls.
2. Observing and processing (blinded and independent):
   • Orientation forward prediction: The environment team uses only environment templates to produce a text forecast card that labels each target as co-aligned/misaligned and states whether an axial perforation corridor is more likely. No access to downstream data.
   • Multi-sector comparisons: The imaging team, at matched angular resolution, constructs axial and orthogonal sectors and computes differences and ratios for RM depth/gradient, emission or dispersion measures, and absorbing columns (report as text intervals).
   • Cross-probe concordance: Independent pipelines for polarization, total-intensity, and absorption each produce axial-minus-control summaries. Teams share only target IDs and sector definitions, not measurements.
   • Arbitration: A third party aligns environment forecast cards with the three result sets and computes hit/wrong/null rates, stratified by co-aligned vs. misaligned and filament/node vs. void categories.
3. Positive/negative controls and removal of false positives:
   • Positive controls:
     1. In co-aligned and filament/node systems, the axial sector shows lower RM depth, smaller emission/dispersion measures, or shallower absorbing columns than the orthogonal sector, and this pattern repeats across probes.
     2. In misaligned or void systems, the axial-versus-orthogonal contrast weakens or vanishes.
   • Negative controls:
     1. Randomly rotate the jet axis (shuffle sectors); axial-orthogonal contrasts should drop to chance.
     2. Point-like calibrators or non-jet morphologies must not exhibit systematic axial dimples.
     3. If strong low-frequency contrasts disappear at high frequency, prefer a foreground-screen or scattering explanation.
   • Separating internal/instrument effects: Use RM synthesis and intra-band differencing to separate intrinsic (jet/lobe) from external (environmental) Faraday contributions. Repeat with multiple calibration and imaging methods (for example, CLEAN, regularized imaging, closure-only). If the effect appears only in one pipeline, classify as spurious.

IV. Systematics and Safeguards (Three Items)

• 3D projection and axis bias: Unknown inclination can dilute co-alignment statistics. Safeguard: constrain inclination using VLBI core structure and apparent superluminal motion; down-weight or hold out high-uncertainty objects.
• Beam smearing and depolarization: Limited resolution and small-scale RM fluctuations can mimic axial depressions. Safeguard: re-measure at multiple resolutions, report a resolution-dependence curve, and run sub-array/down-sampling robustness tests.
• Cosmic-filament extraction bias: Skeleton orientation depends on survey depth and masks. Safeguard: use multiple filament-finding algorithms and Monte Carlo reconstructions; assign a principal-axis confidence grade and stratify statistics accordingly.

V. Execution and Transparency

Pre-register co-alignment criteria, sector definitions, metric lists, positive/negative controls, exclusion rules, and statistical procedures. Keep hold-out subsamples in each environment class for final confirmation. Replicate across arrays and independent processing teams. Publicly release the environment-skeleton axis catalog, jet-axis catalog, and plain-language sector-contrast summaries, plus key intermediate artifacts for outside review. This chapter forms a closed loop with the chapters on frequency-independent path terms, polarization group alignments (“filament-mesh synergy”), and co-window brightness–polarization changes at jet bases; cross-references are required.

VI. Pass/Fail Criteria

1. Support (passes):
   • Co-aligned systems are significantly more common than misaligned ones (|ΔPA| distribution skews to small angles), especially in filament/node environments.
   • In co-aligned systems, axial sectors show stable depressions in RM depth, emission/dispersion measures, or absorbing columns relative to orthogonal sectors, with multi-probe replication.
   • Findings remain robust to band, resolution, array, and pipeline changes, and significantly exceed chance under rotation tests.
2. Refutation (fails):
   • No statistical co-alignment between jets and cosmic filaments, or axial-orthogonal contrasts remain insignificant.
   • Axial differences flip or rescale with frequency (dispersive/Faraday behavior) or are driven mainly by a single array or pipeline.
   • Differences between targets and controls and across environment grades are not significant, undermining an environment-driven perforation claim.