•Jean’s criteria
governs “small scale” collapse due to
self-gravitation
–Treated as stability vs. perturbation in an infinite homogeneous medium in equilibrium
–For fluid
with a pressure P = ρ0vs2, then perturbations with λ > vs(G ρ0)-1/2 = λJ are unstable.
–Basically, does the disturbance have time to cross in a freefall time, tff = (Gρ)-1/2? If so, then pressure forces are negligible.
–The sound crossing time is r/vs, which gives the λJ criteria
–For galaxies, we can write an effective pressure in terms of the velocity dispersion: λ > σ(G ρ0)-1/2 = λJ