Jeans mass
/ JEENZ /
If the Jeans instability tells you that gravity can win, the Jeans mass tells you how much gas you need before it does. It is the tipping-point mass: gather more than this in a clump of gas at a given temperature and density, and gravity overwhelms pressure and the clump collapses; gather less, and pressure holds it up and nothing happens. It is the gatekeeper that decides whether a clump of cloud becomes a star.
The Jeans mass depends on just two things about the gas: its temperature and its density. Colder gas has a smaller Jeans mass, because cool gas pushes back weakly, so even a modest clump can collapse. Denser gas also has a smaller Jeans mass, because packing the mass close together strengthens gravity. Put numbers to it: in a typical cold molecular cloud core, around 10 degrees above absolute zero, the Jeans mass works out to roughly one solar mass, give or take, which is wonderfully close to the mass of a typical star. In a warmer, thinner cloud the Jeans mass might be hundreds or thousands of solar masses, so only very large regions could ever collapse.
The Jeans mass is one of the most satisfying numbers in astrophysics because it naturally explains why stars come out roughly the mass of the Sun rather than the mass of a planet or of a whole galaxy. As a cloud collapses and grows denser while staying cold, its Jeans mass keeps shrinking, so smaller and smaller sub-clumps become unstable in turn; this cascade is the engine behind fragmentation, where one big cloud breaks into many star-sized pieces. The bare Jeans mass ignores turbulence and magnetic support, so it is an order-of-magnitude guide rather than an exact recipe, but it captures why stellar masses cluster where they do.
Cool a clump of cloud from 100 degrees above absolute zero down to 10, keeping its density fixed, and its Jeans mass drops by about a factor of thirty, so a clump that was far too small to collapse can suddenly be heavy enough.
Cooling shrinks the Jeans mass, which is why cold clouds are the ones that make stars.
Remember the Jeans mass is set by temperature and density, not by the cloud's total size: a huge but warm, thin cloud may have a Jeans mass larger than itself and so be perfectly stable.