Galactic Jeans Mass Calculator

Jeans mass and gravitational collapse

Below a certain mass, a cloud of gas can hold itself up against its own gravity; above it, gravity wins and the cloud collapses into a star. That threshold is the Jeans mass, and a self-gravitating cloud has to pass it to beat thermal pressure. Sir James Jeans worked out the expression in 1902: M_J = (5kT / (Gμm_H))^(3/2) · (3/(4πρ))^(1/2), where k is Boltzmann's constant, T temperature, G Newton's constant, μ mean molecular weight, m_H the hydrogen mass and ρ the gas density. Take a cold molecular core at T ≈ 10 K and n ≈ 10³ cm⁻³ as an example. You get M_J in the range of a few solar masses, which lines up nicely with how massive a forming star usually turns out to be. Crank up T and M_J climbs; pack the gas denser and it drops.

Applications

Foundational in star-formation theory: Giant Molecular Clouds (GMCs) fragment into Jeans-unstable clumps that become protostars. Numerical simulations such as IllustrisTNG, FIRE and EAGLE use the Jeans criterion as a sub-grid prescription for when gas should turn into stars. It also explains the initial mass function, the mass distribution of newly formed stars, and constrains models of the first (Population III) stars in the early universe.

FAQ

What is the Jeans length? The companion scale L_J ≈ √(π·c_s²/(G·ρ)), the minimum size for instability; M_J = (4/3)π·(L_J/2)³·ρ.

Does rotation or magnetic field change M_J? Yes — both add support against gravity and raise the effective Jeans mass (magnetic Jeans mass).

Why does cold gas form stars more easily? Lower T directly lowers M_J ∝ T^(3/2); cooling enables fragmentation into many small protostars.

Connection with the Bonnor–Ebert mass? A refined form for isothermal spheres in pressure equilibrium; numerically close to M_J for typical cloud conditions.