A spiral galaxy fed by metric inflow, with polar PG jets

Interactive model after E.P.J. de Haas: constant-Lagrangian disk inflow and the three-rapidity Painlevé–Gullstrand jet cones

disk inflowjet outflowbulge

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Disk

Bulge mass M

Bulge radius R

Redshift z

Broad inflow cones θ = π/2 ∓ δ

H(z)
Critical radius r_c
v_L (outside bulge)
Pitch α at 10 kpc

Jet

w_θ₀(r) = −√(2GM/r) + v_φ cot θ₀ θ_jet = arctan(v_φ/v_esc)

Opening angle θ₀

Outflow speed w_out/v_esc (helix pitch)

Surplus redirected into jets

v_φ/v_esc = tan θ₀
Helix turns, launch → jet tip

θ₀ = 6° gives v_φ = 0.105 v_esc, the M87 constraint. The papers fix v_φ and θ₀ but not the outward speed on the cone, so w_out and the surplus fraction are free display parameters here.

View

Flow speed

About this model

Disk: constant-Lagrangian metric inflow, v_L = v_orb φ̂ − v_rad,eff r̂, with the bulge (r ≤ R) and disk (r > R) expressions; arms are streamlines of this flow. H(z) from flat ΛCDM (H₀ = 70, Ω_m = 0.3).

Jets: stationary PG cone flow; surplus inflow the bulge cannot absorb leaves along narrow polar cones as double-helix streamlines with a spine–sheath structure.

Schematic, not to scale: the launch region is sub-parsec and is magnified here; jet speed runs on its own display clock. Disk tracers move at 3 Myr per frame at flow speed 1.

de Haas, JHEPGC 11 (2025) 1592, doi:10.4236/jhepgc.2025.114097 · JHEPGC 12 (2026) 334, doi:10.4236/jhepgc.2026.121022 · PG Bernoulli jets (2025) · PG jet of M87 (2025).