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.
[1] The Toomre Q parameter is often defined as the left-hand side of Eq.1, The stability criterion can then simply be stated as,
Many astrophysical objects result from the gravitational collapse of gaseous objects (for example, star formation occurs when molecular clouds collapse under gravity), and thus the stability of gaseous systems is of great interest.
The most basic gravitational stability analysis is the Jeans criteria, which addresses the balance between self-gravity and thermal pressure in a gas.
The Toomre analysis, first studied by Viktor Safronov in the 1960s,[2] considers not only gravity and pressure, but also shear forces from differential rotation.
Conceptually, if a fluid is differentially rotating (such as in the keplerian motion of an astrophysical disk), gravity not only has to overcome the internal pressure of the gas, but also needs to halt the relative motion between two parcels of fluid, allowing them to collapse together.