= Solution
In the <Toomre stability criterion>
$$
Q=\frac{\Omega c_s}{\pi G\Sigma},
$$
the disk's <gravitational potential> supplies the destabilizing attraction, <gas pressure> represented by $c_s$ suppresses short wavelengths, and the <Keplerian shear> represented by the <angular frequency> $\Omega$ prevents coherent collapse on long scales through epicyclic motion. Axisymmetric perturbations are stable for $Q>1$ and gravitationally unstable for $Q<1$.
The state $Q\sim1$ is a self-regulating fixed point. If cooling lowers $c_s$ until $Q<1$, gravitational instability produces shocks and turbulence that heat the disk and raise its effective velocity dispersion. If $Q$ becomes appreciably larger than one, the instability and its heating switch off, while turbulent dissipation and radiative cooling reduce $c_s$. A sustained gravito-turbulent state therefore remains close to marginal stability.
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