= Weak-drag secular gravitational growth rate
{title2=$s_{\mathrm{sec}}=\epsilon\Omega(\Omega^2-\omega^2)/\omega^2+O(\epsilon^2)$}
The mode originating at the neutral root grows for $0<\omega^2<\Omega^2$. At small nonzero $|k|$ this gives $s_{\mathrm{sec}}\sim2\pi\epsilon G\sigma_0|k|/\Omega$. <Gas drag> transfers angular momentum to the fixed gas flow and permits <secular gravitational instability> even for a dust <Toomre parameter> above unity. If $\omega^2<0$, the small-root continuation is damped, while a separate dynamical root grows. The formula is singular at $\omega^2=0$.
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