•Stability
on all scales
–Combine
the criteria for large and small scales
–Need a
minimum velocity dispersion to make critical Jean’s length equal to Lcrit.
–Order of magnitude then, write Jean’s length in
terms of surface density by
equating free fall and crossing times: λJ = σ2/Gμ = Lcrit, or σ=Gμ/Ω
–A more rigorous
calculation gives σr=3.36Gμ/κ, where κ is the epicyclic
frequency (see below)
–Ratio of observed radial dispersion to
critical dispersion is called Q, and stability requires Q >
1.
–Near the Sun, Q is between 1 and 2.
–