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. W e 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 dist ribution, taking into account the finite extent of the background source an d the incomplete sampling of optical depth over the extent of the source. W e 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 towar d 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 var iations on small transverse scales.