OURANOS · the celestial · the sky, measured · kept by URANIA

THE JEANS MASS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

Stars are born when a cloud of gas collapses under its own gravity — but only if it’s heavy enough. Gravity pulls the cloud inward; the gas’s pressure pushes back out. Below a critical mass (the Jeans mass) pressure wins and the cloud just sits there; above it, gravity wins and the cloud falls in on itself to ignite a star. COLD, DENSE clouds collapse easiest. Slide the conditions and watch the cloud tip over the edge.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ WHEN A CLOUD FALLS · 3D · gravity vs pressure, and a star is born
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
Jeans mass
cloud mass
gravity vs pressure
COLLAPSES?

◆ LIT — exact / checkable

A gas cloud collapses to form stars only if its gravitational self-attraction overcomes its internal (thermal) pressure. The threshold is the JEANS MASS, Mᵢ ∝ T³⁄² / √ρ (temperature T, density ρ): a cloud more massive than Mᵢ is unstable and collapses. So the Jeans mass FALLS for colder, denser gas — which is why star formation happens in cold molecular clouds, and why a cloud that cools or is compressed (by a shockwave, a nearby supernova) can be pushed over its Jeans mass and fragment into stars. A fail-loud self-check throws unless the Jeans mass is lower for cold, dense gas than for warm, thin gas. ◆ real astrophysics, node-verified.

▲ AMBER — the figure

The Jeans criterion scaling Mᵢ ∝ T³⁄²ρ⁻¹⁄² (exact for a uniform cloud; magnetic fields and turbulence modify the real threshold); the cold-and-dense-collapses-easier result is exact.

OURANOS: the sky is a laboratory you may only look at — so we learned to weigh it with light.  — URANIA
David Lee Wise / ROOT0 / TriPod LLC  ·  the observatory, with AVAN