Growth of Fluctuations in a Uniformly Contracting or Expanding Cloud.
Abstract
Since no gas sphere in hydrostatic equilibrium is unstable to radially symmetric perturbations, provided that F > 4 and that the density increases with depth, the stability of a model without hydrostatic equilibrium is investigated. This model has been discussed by Ebert and Bonnor and is characterized by a uniform density, pressure, and expansion or contraction. Since in the absence of pressure gradients each element is in free fall, one erroneously expects that Jeans's criterion determines stability. For the zeroenergy case (corresponding to parabolic motion), the system is unstable for all F < 4 independent of the Jeans criterion. For expansion, the Jeans criterion separates unstable from stable motion when F = 4, while for all larger values of F the motion is unstable, independent again of the Jeans criterion. Exact solutions are given for nonzero energy (elliptical and hyperbolic motion) for special values of F, and asymptotic solutions valid for several ranges of F are given. The existence of unstable solutions suggests, but does not prove, the possibility of fragmentation into stable protostars or protogalaxies
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1962
 DOI:
 10.1086/147411
 Bibcode:
 1962ApJ...136..609S