Power spectrum of the density of cold atomic gas in the Galaxy toward Cassiopeia A and Cygnus A

We have obtained the power spectral description of the density and opacity fluctuations of the cold H I gas in the Galaxy toward Cas A and Cygnus A. We have employed a method of deconvolution, based on CLEAN, to estimate the true power spectrum of optical depth of cold H I gas from the observed distribution, taking into account the finite extent of the background source and the incomplete sampling of optical depth over the extent of the source. We investigate the nature of the underlying spectrum of density fluctuations in the cold H I gas which would be consistent with that of the observed H I optical depth fluctuations. These power spectra for the Perseus arm toward Cas A and for the outer arm toward Cygnus A have a slope of 2.75 +/- 0.25 (3 sigma error). The slope in the case of the Local arm toward Cygnus A is 2.5 and is significantly shallower in comparison. The linear scales probed here range from 0.01 to 3 pc. We discuss the implications of our results, the non-Kolmogorov nature of the spectrum, and the observed H I opacity variations on small transverse scales.