4.6 How the Cortex Appears and Speaks: Rings, Polarization, and Common Timing

Home ／ Chapter 4: Black Holes

Reader’s note. This section targets readers who already know black hole observations and near-horizon physics. We pair what is seen with how it forms, and we list practical checks for identification and de-bugging.

I. Image-Plane Signatures: Main Ring, Sub-Rings, and the Long-Lived Bright Sector

1. Main ring — strong stacking from multi-pass returns near the critical band
   • Phenomenology: A bright ring surrounds a central shadow. The ring radius is nearly constant across epochs, while thickness varies with azimuth.
   • Mechanism: As a line of sight crosses the tensile cortex, light is repeatedly bent near the critical band. Near-grazing, multi-pass returns and long-path stacking build up geometrically. When emissive material skirts the band, energy along the sightline accumulates and forms a stable luminous ring. The radius tracks the band’s average position (thus stable); thickness follows local retreat and the number of return layers (thus azimuthal structure).
   • Identification: After cross-reconstruction, fit a simplified ring model and compare radii across nights and frequencies. Check closure phase and closure amplitude to exclude array-geometry artifacts.
2. Sub-rings — a deeper series of return orders
   • Phenomenology: Fainter, thinner, concentric rings appear inside the main ring, requiring higher dynamic range.
   • Mechanism: Some rays make one or more additional returns inside the band, then exit through small retreat windows. Distinct return orders map to different path lengths and exit angles, projecting as secondary fine rings—more inward, thinner, dimmer.
   • Identification: Look for a second shallow minimum in the visibility curve; subtract a main-ring model and test whether residuals show a positive ring; co-located detections across frequencies raise confidence.
   • Pitfalls: Rule out scattering tails and deconvolution artifacts; rely on closure quantities and multi-algorithm consistency.
3. Long-lived bright sector — a statistical “soft spot” of reduced criticality
   • Phenomenology: One sector of the ring stays brighter with a relatively fixed position; the contrast is measurable.
   • Mechanism: In that azimuth, shear in the transition zone aligns micro-ripples and creates a band-like subcritical corridor; the tensile cortex retreats slightly more easily there. Effective outward resistance falls, so multi-pass energy escapes more readily and the sector stays bright.
   • Identification: Persistent enhancement at the same azimuth across nights and bands, often co-located with banded polarization features.
   • Pitfalls: Vary initial models and uv-coverage to test whether the sector “follows the algorithm.” If its azimuth drifts with imaging setup, treat it with caution.

II. Polarization Patterns: Smooth Twists and Banded Flips

1. Smooth twist — projection of shear-aligned geometry
   • Phenomenology: The electric vector position angle (EVPA) varies smoothly along the ring, often nearly monotonic by segment.
   • Mechanism: The transition zone straightens small ripples into strips. The observed EVPA reflects strip orientation and local propagation geometry. As azimuth changes, projection changes continuously, and EVPA twists smoothly.
   • Identification: Build a rotation-measure map to remove foreground Faraday rotation; then sample EVPA uniformly along the ring and plot EVPA versus azimuth. Expect a smooth, non-jumpy curve.
2. Banded flips — narrow imprints of reconnection corridors and orientation reversals
   • Phenomenology: One or more narrow bands show rapid EVPA flips and reduced polarization fraction; a matching narrow stripe often appears in total intensity.
   • Mechanism: In corridors of active reconnection or sharp shear transitions, the dominant source orientation reverses on small scales, or opposite orientations mix along one sightline. Their superposition flips net EVPA and lowers the fraction.
   • Identification: Positions should agree across nearby bands; flip-band width is clearly smaller than the ring width; locations often coincide with edges of the long-lived bright sector or shear corridors in the transition zone.
   • Pitfalls: Remove Faraday rotation by multi-band linear extrapolation and check if the flip remains co-located. Verify instrumental polarization leakage to avoid mistaking calibration residuals for true flips.

III. Time-Domain “Voices”: Common Steps and Echo Envelopes

1. Common step — synchronized gating of the entire critical ring
   • Phenomenology: After de-dispersion and alignment, multi-band light curves jump or kink at nearly the same time.
   • Mechanism: A strong event presses the tensile cortex slightly downward, lowering the critical threshold for a short time. Multi-pass energy escapes more easily across nearly all bands. Because this is geometric gating, not dispersive transport, the timing is cross-band synchronous.
   • Identification: After alignment, cross-correlate residuals; expect a significant zero-lag peak independent of frequency. In images from the same window, the bright sector often strengthens and banded polarization becomes more active.
   • Pitfalls: Exclude pipeline synchronizations and calibration step changes; confirm the step is not a saturation or clipping artifact in a single band.
2. Echo envelope — rebound after retreat with multi-pass re-routing
   • Phenomenology: Following a strong event, secondary peaks appear with shrinking amplitudes and growing separations.
   • Mechanism: The transition zone stores input as local tension lifts, then releases in batches while geometric loops re-route paths. The first release is largest; each subsequent one weakens. As paths lengthen, intervals grow. If an inner rebound coexists, two rhythms superpose, broadening the envelope.
   • Identification: Use autocorrelation or wavelets to locate secondary peaks; test cross-band phase alignment; verify that interval growth is consistent across bands.
   • Pitfalls: Check for coupling to diurnal backgrounds or uv-windowing; remove periodic scanning or focus-stepping artifacts.

IV. Minimal Three-Step Discrimination and Troubleshooting

1. Instrument and reconstruction
   • Cross-reconstruction: switch algorithms and starting models; test whether main ring, sub-rings, and bright sector persist.
   • Closure quantities: use closure phase and closure amplitude to verify that key structures are astrophysical.
   • Snapshot imaging: for fast sources, shorten synthesis to avoid smearing time variability into spatial texture.
2. Foreground and medium
   • Faraday correction: build a rotation-measure map, recover intrinsic EVPA, then assess twists and flip bands.
   • Scattering assessment: compare size–frequency trends to exclude scattering blur and extrapolation illusions.
3. Multi-domain consistency
   • Cross-evidence: do the common step, bright-sector strengthening, and flip-band activity co-occur?
   • Multi-site and multi-night stability: do key fingerprints remain under different array geometries and epochs?

V. In Summary: One Cortex, Three Languages

• The main ring and its sub-rings arise from geometric stacking on the critical band; the persistent bright sector marks a band-like statistical weak spot of reduced criticality.
• The smooth twist records strip orientations after shear alignment; the banded flip is a narrow imprint of reconnection corridors or orientation reversals.
• The common step and echo envelope are the time-domain faces of a ring-wide threshold being pressed and then rebounding.

Viewed together, these strands align “what we see” with “why it happens”: the same tensile cortex writes rings and bands on the image plane, orientations in polarization, and gating plus echoes on the time axis. This mapping underpins the channel mechanics and energy-sharing rules developed later.