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In astrophysics, Toomre's stability criterion is a relationship between parameters of a differentially rotating, gaseous accretion disc which can be used to determine approximately whether the system is stable. In the case of a stationary gas, the Jeans stability criterion can be used to compare the strength of gravity with that of thermal pressure. In the case of a differentially rotating disk, the shear force can provide an additional stabilizing force.
The Toomre criterion for a disk to be stable can be expressed as,
where c s {\displaystyle c_{s}} is the speed of sound , κ {\displaystyle \kappa } is the epicyclic frequency, G is Newton's gravitational constant, and Σ {\displaystyle \Sigma } is the surface density of the disk.
The Toomre Q parameter is often defined as the left-hand side of Eq.1,