Astrophysical Jets: Topological Collimation from T² Fibration
Relativistic polar jets arise from T² topology: the fibration forces matter into an equatorial accretion funnel and reserves the polar axis as a 1D topological channel. The Jet Collimation Theorem (Book V ch40) bounds the opening half-angle by arcsin(ι_τ) ≈ 19.96°.
Overview
Relativistic jets from accretion disks — seen in AGN, microquasars, and gamma-ray bursts — are a longstanding open problem: why do certain compact objects launch narrow polar jets at near-luminal speeds, and what sets their collimation? Book V ch40 (“Accretion, Jets, AGN”) derives jet structure topologically. The T² fibration over the compact object forces infalling matter into an equatorial accretion funnel while reserving the polar axis as a one-dimensional topological channel. The Jet Collimation Theorem bounds the opening half-angle by arcsin(ι_τ) ≈ 19.96°. The AGN Unification Theorem in the same chapter replaces the orthodox orientation-based unification with a classification by coherent-instance lifecycle phases.
Detail
The orthodox picture of astrophysical jets involves Blandford-Znajek-type magnetic extraction of rotational energy from a black hole, with collimation supplied by magnetic tension or external pressure — but the quantitative emergence of narrow polar jets from equatorial accretion flow is not first-principles predicted. Book V ch40 (books/V-CategoricalMacrocosm/latex/sections/part05/ch40-accretion-jets-agn.tex) treats the problem as a topological readout of T² over the compact object. The fibration structure forces matter into the equatorial plane (the accretion funnel) and reserves the polar axis as a 1-dimensional topological channel — geometrically constrained, not magnetohydrodynamically forced. The Jet Collimation Theorem proves that the opening half-angle is bounded by arcsin(ι_τ), where ι_τ = 2/(π+e) is the master constant; numerically this gives ~19.96°, consistent with observed narrow-jet morphologies. The AGN Unification Theorem in the same chapter classifies AGN types (blazar, radio galaxy, Seyfert, quasar) by their position in the coherent-instance lifecycle rather than by ad hoc orientation assumptions — removing an arbitrary degree of freedom from the orthodox unified model. The topological mechanism also predicts specific polarization signatures that are observationally testable.
Result Statement
Jet Collimation Theorem (Book V ch40): T² fibration forces equatorial accretion and polar 1D channel. Opening half-angle ≤ arcsin(ι_τ) ≈ 19.96°. AGN Unification Theorem replaces orientation-based with lifecycle-based classification.