The Rayleigh-Taylor Instability in Compressible Fluids.

National Radio Astronomy Observatory, Green Bank, West Virginia (now at Princeton University Observatory) .-The Rayleigh-Taylor instability of an isothermal atmosphere supported against gravity by a uniform inCompressible fluid has been analyzed. A perturbation characterized by a periodic deformation of the boundary separating the two fluids is found to grow like exp ~), and the dependence of the growth rate ~ on the wavelength A of the perturbation is determined. For very short wavelengths, ~ is proportional to A-~ (as is the case for all wavelengths when both fluids are incompressible) ; whereas for long wavelengths ~ is proportional to A-1. Thus, the effect of compressibility is to retard the growth rates for the longest wavelengths. The transition from the A-1-dependence to the A~2-dependence of ~ occurs in a range of wavelengths of order Ac, where Ac is a determinate quantity in the theory. If the Raleigh-Taylor instability can occur at the boundary of an expanding Hii region, the present model is a reasonable first approximation to the physical situation in the sense that compressibility is important mainly in the surrounding Hi region (the upper fluid). Since the growth rates of perturbations having long wavelengths are retarded, Ac is the order of the longest wavelength with which the Rayleigh-Taylor instability is likely to be observed in an Hii region. If the temperature of the Hii region is 10 0000K, and if the acceleration of the boundary of the Hii region lies in the range 4 X 10-~ cm/sec2 to 4 X 10-~ cm/sec2, then Ac lies in the range 8 pc to 80 PC. These values are to be compared with the maximum observed widths of the order of 6 pc for the so-called "elephant trunk" structures which are found in Hii regions. The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under contract with the National Science Foundation.