Jeans instability

Jeans instability is the growth of density perturbations in a self-gravitating gas when gravity overcomes pressure support, potentially leading to gravitational collapse.

Jeans length: The critical wavelength above which density perturbations in a uniform gas can grow under self-gravity. Perturbations larger than this scale can outrun pressure support and collapse.
Star formation: The process by which dense regions of interstellar gas collapse and produce stars. Jeans-unstable gas clouds can begin the collapse that forms stars.
Self-gravitating gas: A gas whose internal mass distribution generates a gravitational field that affects its motion. Jeans instability describes how perturbations evolve in this kind of medium.
Toomre instability: A local gravitational instability criterion for rotating, differentially rotating disks. Rotation and shear add stabilizing effects absent from the basic Jeans analysis.
Jeans mass: The critical mass of a gas region whose self-gravity can overcome pressure support under specified conditions. It expresses the instability threshold as a mass rather than a wavelength.
Molecular cloud: A cold, dense interstellar cloud composed largely of molecular hydrogen and dust. Its dense regions can cross the Jeans threshold and fragment.
Fluid equations: Equations describing the motion and conservation of mass, momentum, and energy in a fluid. Linearized fluid equations yield the pressure and gravity terms in the instability criterion.
Magneto-Jeans instability: Gravitational instability in a magnetized gas, where magnetic forces alter the growth of perturbations. It extends the Jeans setting by including magnetic-field forces.
Jeans swindle: The mathematical device of neglecting a uniform gravitational background when analyzing perturbations in an infinite homogeneous medium. It exposes a foundational inconsistency in the simplest derivation of the instability.
Bonnor–Ebert sphere: A pressure-confined, isothermal gas sphere whose stability depends on its mass and boundary pressure. It describes stability for a finite cloud, unlike the idealized uniform medium in Jeans analysis.

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