38 Co-Located “Slow-Leak Spectrum” of Galactic Nucleus Outflows and Pore-Breathing

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. Under unified time/frequency standards and source-end calibration, we define a reproducible slow-leak spectrum for multi-phase nuclear outflows (ionized/neutral/molecular): a low-velocity, extended plateau or gently leaking constant term in velocity–radius–phase space that is nearly non-dispersive across bands and lines. We then test whether this fingerprint is co-located in time and azimuth with pore-breathing (Chapter 26): when near-nuclear/near-horizon windows show co-window time-delay co-occurrence, polarization flips, or phase breathing (Chapters 7 and 22), does the outflow base and large-scale leakage strengthen synchronously or show threshold-like jumps? If stellar-wind episodes, dust radiative transfer, beam dilution/PSF mixing, or bandpass/color mis-calibration explain the signals—or replication fails across lines/arrays/teams—the claim is disfavored.

I. One-Sentence Goal

Establish a non-dispersive slow-leak fingerprint in nuclear outflows and test co-window co-location with horizon-proximate pore-breathing, favoring a common path term over conventional stellar/dust mechanisms.

II. What to Measure

• Slow-leak index (text grades):
  After common beam/bandpass/spectral resolution, measure low-velocity constant terms and gentle leakage slopes in velocity and radial profiles. Grade strong / medium / weak; uplift / depression for single sources and stacks (binned by mass/accretion/redshift/environment), and record velocity thresholds and plateau spans.
• Non-dispersion across lines/bands:
  Test rank/sign stability in [O III]/Hα/Na D/Fe II (ionized/neutral), OH 119 μm/HCN/HCO⁺/CO(1–0)/(3–2) (molecular), and X-ray warm absorbers. Systematic flips/scalings with carrier or optical depth imply dispersion/radiative-transfer origins.
• Zero-lag co-location (aligned windows):
  Using a single external timescale, align mm/cm polarization time series, radio-core brightness, RM variations, NIR/optical variability, and the slow-leak index. Grade zero-lag peaks and side-lobe contrast; co-window, same-direction concurrence with pore-breathing supports the claim.
• Morphology–radius robustness:
  In biconical/disk, jet–outflow co-linear vs non-co-linear samples, test whether the slow-leak constant forms a radial plateau and is insensitive to morphology/inclination; confinement to single sectors/substructures downgrades confidence.
• Environment linkage and stratification:
  Cross-match with host filament orientation, lensing κ–γ background, large-scale density, ISM surface density, and nuclear SFR; tag enhance / plateau / uncorrelated and stratify by Eddington ratio, black-hole mass, jet power.
• Ratio robustness and template orthogonality:
  Validate “rigid shift, ratio unchanged”—stable line/phase ratios with significant absolute leakage constants—and near-orthogonality to stellar-wind/dust-scattering/surface-brightness-gradient templates.
• Seasonal/yearly reproducibility and event response:
  Test multi-year stability and responses during flares/state changes/merger triggers, noting threshold-like behavior.

III. How to Do It

1. Data and arrays:
   • Optical/NIR IFU: MUSE/KCWI/MEGARA/SINFONI spectral cubes.
   • mm/submm interferometry: ALMA/NOEMA (CO/HCN/HCO⁺/OH) with a common synthesized beam.
   • cm radio and polarization: VLA/eMERLIN/VLBA for core brightness, EVPA, RM variability, core shift.
   • X-ray absorption/emission: Chandra/XMM-Newton/XRISM for warm absorbers/thermal phases.
   • Auxiliary layers: lensing κ/γ, host-filament maps, SFR/Σ_gas, dust/radio templates, and time-domain light curves.
2. Unified calibration and de-systematics:
   • Beam/bandpass/color: publish per-channel beams/sidelobes and bandpass kernels/color corrections; convolve to a common beam and hold out band edges.
   • Spectroscopy: standardize continuum subtraction/sky lines/PSF deblending; marginalize optical depth/covering factor.
   • Dual path (velocity vs phase): (a) constrained ILC/template regression suppressing stellar winds/dust/scattering while preserving color-flat degrees; (b) parametric matched-filter fitting joint multi-phase outflow; run blind to each other.
   • Time alignment: lock to a single atomic time/1PPS, build co-window/co-kernel grids for polarization/brightness and slow-leak indices.
3. Sequence construction and comparison:
   • Per source × line × array × window, tabulate slow-leak index and zero-lag index (text grades).
   • Profiles/stacks: stack by Eddington ratio/BH mass/environment; output radial-plateau stability and cross-line color flatness.
   • Differencing/orthogonality: run contrasts versus stellar-wind/dust/brightness-gradient/beam-dilution templates; require near-orthogonality.
4. Forward prediction, blinding, arbitration:
   • Environment-forward team: using only filament orientation/lensing/Σ_gas/SFR and masks, issue prediction cards (slow-leak direction/strength, non-dispersion, co-window with pore-breathing, threshold expected).
   • Measurement teams (independent pipelines): run ≥ 2 cleaning paths and two alignment strategies without sharing residuals.
   • Arbitration: align predictions with results; compute hit / wrong / null rates by line/array/season/method.
5. Cross-consistency:
   • Check co-window/azimuth with Chapter 26 (pore-layer tomography).
   • Align polarization/time-delay criteria with Chapters 7 and 22.
   • Compare spatial tags with Chapters 8/32 (host filament alignment synergy).

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (support slow-leak ↔ pore-breathing co-location):
   • Across multiple lines/arrays, detect same-sign, stable low-velocity plateaus or gentle leakage constants with zero-lag co-occurrence after alignment.
   • Non-dispersion: insensitivity to carrier/optical depth/band edges with stable ratios.
   • Co-window, same-direction concurrence with pore-breathing or a physically interpretable short lag consistent with propagation/geometry.
   • Prediction-card hit rates above chance; replication across methods/arrays/years.
2. Negative controls (against co-location):
   • Residuals follow frequency/optical-depth laws (dust/radiative transfer/saturation) or appear in one line only.
   • High sensitivity to beam/bandpass/PSF deblending/alignment/window choices.
   • Label swaps/time reversal/position rotation/parameter shuffles still yield “detections,” indicating selection/method bias.
   • Signals vanish after stellar-wind/dust template boosts, deep masks, or band-edge hold-outs.

V. Systematics and Safeguards (Three Items)

• Radiative-transfer and optical-depth degeneracies: can fake low-velocity plateaus. Safeguard: pair different-depth lines/isotopologues (e.g., ¹³CO), use P-Cygni diagnostics, and perform inject–recover calibration.
• Beam/PSF–spectral mixing and beam dilution: blends space and velocity. Safeguard: common-beam convolution, uv-plane modeling, and PSF-variant/ subset-hold-out robustness.
• Timing mis-registration (polarization–spectroscopy): breaks co-window claims. Safeguard: single external timescale, quasi-simultaneous scheduling, out-of-window hold-outs, and prewhitened cross-correlation.

VI. Execution and Transparency

Pre-register sources/lines/arrays, common beam/bandpass kernels and spectral processing conventions, criteria for non-dispersion/zero-lag/radial plateau/co-window, environment variables and stratification, positive/negative controls, exclusions, and arbitration. Define held-out units (jet–outflow co-linear vs non-co-linear, high-Σ_gas vs low-Σ_gas, flare windows, merger candidates). Enable cross-team/array replication through spectral cubes/uv data/polarization series/masks/logs/scripts; run down-sampling/noise/kernel-variant/alignment-perturbation tests. Publicly release prediction cards, slow-leak index tables, zero-lag/non-dispersion summaries, and beam/bandpass/color/PSF logs with key intermediates.

VII. Pass/Fail Criteria

1. Support (passes):
   • In ≥ 2 pipelines, ≥ 2 arrays, ≥ 3 phase/line families, recover a non-dispersive slow-leak plateau/leakage constant with zero-lag co-occurrence.
   • Co-window, same-direction concurrence with pore-breathing or a short, physically explainable lag; monotonic/threshold relations with jet/filament/environment strength.
   • Robust to beam/bandpass/PSF/alignment/mask choices, and replicates in held-out units with prediction-card hits above chance.
2. Refutation (fails):
   • Dominance by dust/radiative transfer/stellar winds or single-line/single-array/single-season detections.
   • Parameter fragility or disappearance in held-out units.
   • Arbitration hits near chance; signals are indistinguishable from method/system artifacts.