Velocity modification of HI power spectrum

The distribution of atomic hydrogen in the Galactic plane is usually mapped using the Doppler shift of 21 cm emission line, and this causes the modifi cation of the observed emission spectrum. We calculate the emission spectru m in velocity slices of data (channel maps) and derive its dependence on th e statistics of velocity and density fields. We find that, (1) if the densi ty spectrum is steep, i.e., n < -3, the large k asymptotics of the emissivi ty spectrum are dominated by the velocity fluctuations; and (2) the velocit y fluctuations make the emission spectra shallower, provided that the data slices are sufficiently thin. In other words, turbulent velocity creates sm all-scale structure that can erroneously be identified as clouds. The effec t of thermal velocity is very similar to the change of the effective slice thickness, but the difference is that, while an increase of the slice thick ness increases the amplitude of the signal, the increase of the turbulent v elocity leaves the measured intensities intact while washing out fluctuatio ns. The contribution of fluctuations in warm H I is suppressed relative to those in the cold component when the velocity channels used are narrower th an the warm H I thermal velocity and small angular scale fluctuations are m easured. We calculate how the spectra vary with the change of velocity slic e thickness and show that the observational 21 cm data is consistent with t he explanation that the intensity fluctuations within individual channel ma ps are generated by turbulent velocity fields. As the thickness of velocity slices increases, density fluctuations begin to dominate emissivity. This allows us to disentangle velocity and density statistics. The application o f our technique to Galactic and SMC data reveals spectra of density and vel ocity with power law indexes close to -11/3. This is a Kolmogorov index, bu t the explanation of the spectrum as due to the Kolmogorov-type cascade fac es substantial difficulties. We generalize our treatment for the case of a statistical study of turbulence inside individual clouds. The mathematical machinery developed is applicable to other emission lines.