Turbulence Statistics from Spectral Line Observations

Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent velocities. We discuss Velocity-Channel Analysis (VCA) and its offspring Velocity Coordinate Spectrum (VCS) that are based on the analytical description of the spectral line statistics. Those techniques are well suited for studies of supersonic turbulence. We stress that a great advantage of VCS is that it does not necessary require good spatial resolution. Addressing the studies of mildly supersonic and subsonic turbulence we discuss the criterion that allows to determine whether Velocity Centroids are dominated by density or velocity. We briefly discuss ways of going beyond power spectra by using of higher order correlations as well as genus analysis. We outline the relation between Spectral Correlation Functions and the statistics available through VCA and VCS.