= Finite-size secular gravitational criterion
{title2=$Q\lesssim L/H$}
For a dust layer of extent $L$, its smallest admissible wavenumber is of order $1/L$. The <secular gravitational instability> band ends at $k_{\mathrm{crit}}=2\pi G\sigma_0/c^2=2/(QH)$, with <Toomre parameter> $Q=c\Omega/(\pi G\sigma_0)$ and $H=c/\Omega$. Requiring an admissible mode in the band gives $Q\lesssim L/H$. Boundary conditions fix the order-unity prefactor; a finite disk lifetime also limits practical growth.
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