= Toomre stability radius of a flat-rotation disk
{c}
{title2=$r_Q=\sqrt2v_0a_0/(\pi G\Sigma)$}
For constant circular speed $v_0$, <angular velocity> is $v_0/r$ and <radial epicyclic frequency> is $\sqrt2v_0/r$. Constant effective random speed and <surface density> then give $Q=r_Q/r$. The local axisymmetric fluid model is stable inside $r_Q$ and unstable outside it. This statement is conditional on the thin-disk local approximation, rather than a proof of global or collisionless stability.
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