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Fluctuations along Velocity Coordinate : Statistics and Effects of Absorption

We discuss statistics of Doppler-broadened spectral lines, in particular, the statistics of fluctuations in Position-Position-Velocity data cubes along the velocity axis. We show that absorption substantially changes the long wavelength statistics of fluctuations compared to the optically thin case. At the same time, short-wavelength asymptotic is not affected by absorption and remains power-law. We consider both the case of high spatial resolution and the case of poor spatial resolution and discuss the retrieval of power-law indexes of velocity and density spectra. This provides a new technique for studies of turbulence from observations. A big advantage of the technique is that studies of turbulence can be accomplished even when spatial resolution of the turbulent volume is poor.