Jeans instability

Star formation
Object classes
Interstellar medium Molecular cloud Bok globule Dark nebula Young stellar object Protostar Pre-main-sequence star T Tauri star Herbig Ae/Be star Herbig–Haro object
Theoretical concepts
Accretion Initial mass function Jeans instability Kelvin–Helmholtz mechanism Nebular hypothesis Planetary migration
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The Jeans instability is a concept in astrophysics that describes an instability that leads to the gravitational collapse of a cloud of gas or dust.^[1] It causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent the gravitational collapse of a region filled with matter.^[2] It is named after James Jeans.

For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to $${\displaystyle {\frac {dp}{dr}}=-{\frac {G\rho (r)M_{\text{enc}}(r)}{r^{2}}},}$$ where ${\textstyle M_{\text{enc}}(r)}$ is the enclosed mass, ${\textstyle p}$ is the pressure, ${\textstyle \rho (r)}$ is the density of the gas (at radius ${\textstyle r}$), ${\textstyle G}$ is the gravitational constant, and ${\textstyle r}$ is the radius. The equilibrium is stable if small perturbations are damped and unstable if they are amplified. In general, the cloud is unstable if it is either very massive at a given temperature or very cool at a given mass; under these circumstances, the gas pressure gradient cannot overcome gravitational force, and the cloud will collapse.^[3] This is called Jeans collapse criterion.

The Jeans instability likely determines when star formation occurs in molecular clouds.