Jet Magnetic Field Ratio B_z/B_φ

τ-Formula

B_z/B_φ = fiber/base ≈ ι_τ ≈ 0.3

Derivation

At the jet base ($∼ 10\,R_S$), the axial-to-toroidal magnetic field ratio is

This follows from the torus hoop-stress collimation: the toroidal component $B_$ provides hoop stress $P = B_^2/(4π r)$ that collimates the jet, while the axial component $B_z$ originates from the topologically protected $Φ_pol$. The equilibrium condition $θ_jet ≤ B_z/B_ = ι_τ$ independently recovers the jet collimation angle $θ_jet ≤ 20^$ (Theorem (thm:ch40-jet-hoop-stress)).

VLBI observations of AGN jets at sub-parsec scales measure $B_z/B_ ∼ 0.2$–$0.5$, consistent with the $τ$-prediction $ι_τ ≈ 0.341$. The ratio is a zero-parameter prediction, testable with improved VLBI polarimetry.

Source

This prediction is derived in the Physics Ledger (Chapter 64 — black-hole-topology), Books IV–V of Panta Rhei.