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Singular isothermal sphere

What you are seeing: the Jeans-equation solution for an isothermal, self-gravitating sphere has ρ∝r−2\rho \propto r^{-2}, M(<r)∝rM(\lt r) \propto r, and a flat circular-velocity curve vc=2σv_c = \sqrt 2 \sigma. This is the canonical "flat rotation curve" of an isothermal halo.

Figure 1. Rotation curve flat at 2σ\sqrt 2 \sigma.
σ (km/s)200

WHAT TO TRY

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