Velocity Modification of HI Power Spectrum

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Abstract
The distribution of atomic hydrogen in the Galactic plane is usually mapped using the Doppler shift of 21cm emission line. We calculate the emission spectrum in velocity slices of data (channel maps) and derive its dependence on the statistics of HI velocity and density fields. We find that (a) if the density spectrum is steep, i.e. n<-3, the short-wave asymptotics of the emissivity spectrum is dominated by velocity fluctuations; (b) the velocity fluctuations make the emission spectra shallower, provided that the data slices are sufficiently thin. In other words, turbulent velocity creates small scale structure that can erroneously be identified as clouds. The contribution of fluctuations in warm HI is suppressed relative to cold component when velocity channels used are narrower than warm HI thermal velocity and small angular scale fluctuations are measured. We calculate how emission spectra vary with the change of velocity slice thickness and show that the observational 21cm data is consistent with the explanation that intensity fluctuations within individual channel maps are generated by a turbulent velocity field. As the thickness of velocity slices increases density fluctuations get to dominate the emissivity. This allows to disentangle velocity and density statistics. Application of our technique to the Galactic and SMC data reveals spectra of density and velocity with the power law index close to -11/3. This is a Kolmogorov index, but the explanation of the spectrum appealing to the Kolmogorov-type cascade faces 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.

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