Oscillation and collapse of interstellar clouds

The gross internal dynamics of interstellar clouds are studied by means of the tensor virial equations. To evaluate the virial integrals, clouds are approximated as compressible ellipsoids, uniform in density, bounded by external pressure, and with velocities linear in the coordinates. Rigidly rotating spheroidal equilibrium states exist for any external pressure, but those at high pressure are distortionally unstable. Elongated rigidly rotating equiliba also exist, but not if the external pressure is sufficiently high. Numerical integration of the dynamic equations demonstrates that clouds of low angular momentum can collapse by several orders of magnitude in density even while remaining axially symmetric. Collapse with the conservation of angular momentum is also possible for clouds of high angular momentum if they attain a specific elongated configuration. The transition between the behavior of clouds of low and high angular momentum is surprisingly abrupt