The Parker instability in a self-gravitating gas layer

The growth time of a perturbation as a function of its dimensions and initial density are yielded by the derivation and explicit solution of the Parker instability dispersion relation in a self-gravitating, exponential gas layer, with validity for arbitrary gas density, magnetic field strength and cosmic ray pressure. For the observed scale height and sound speed in the interstellar medium, the dimensionless density equals 1.8 times the ambient density, expressed in cu cm. Self-gravity is found to be more important than either magnetic fields or cosmic rays in regions of higher gas density, and cloud formation in the case of such a Parker-Jeans instability can be so fast as to result in star formation in a moderately-compressed interstellar medium within only 20 million years.