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Spiral density-wave dispersion

What you are seeing: the Lin-Shu dispersion relation for tightly-wound spiral density waves: ν2=κ2−2πGΣ∣k∣+k2cs2\nu^2 = \kappa^2 - 2\pi G \Sigma |k| + k^2 c_s^2. Toomre's Q<1Q \lt 1 means ν2<0\nu^2 \lt 0 at some kk: axisymmetric instability.

Figure 1. Dispersion curve ν2(k)\nu^2(k); dips below zero when Q<1Q \lt 1.
σ1.50
κ1.50
2πGΣ3.0

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.