Parker instability in a self-gravitating gas layer

The dispersion relation for the Parker instability in a self-gravitating, exponential gas layer is derived nd solved explicitly to give the growth time of a perturbation as a function of its dimensions and initial density. Our solution is a general result, expressed in dimensionless form, and valid for arbitrary gas density, magnetic field strength and cosmic ray pressure. Self-gravity is important as an additional driving force for the Parker instability when a dimensionless density, defined here, becomes comparable to the ratios of the magnetic and cosmic ray pressures to the thermal gas pressure. For the observed scale height and sound speed in the interstellar medium, the dimensionless density equals 1.8 times the ambient density in cm-3. Self-gravity is marginally important for instabilities in the ambient medium. Self-gravity becomes more important than magnetic fields or cosmic rays in regions of higher gas density. For example, in a spiral density wave shock, where the gas density may be 5 cm-3, the initial growth time of the combined instability is only 12 million years. The instability is dominated by self-gravitational forces at these densities, so this growth time is relatively independent of magnetic field strength and cosmic ray pressure. Cloud formation by this Parker-Jeans instability can be so fast that star formation may occur in a moderately compressed interstellar medium within only 20 million years