Statistics of Turbulence from Spectral-Line Data Cubes

Emission in spectral lines can provide unique information on interstellar turbulence. Doppler shifts due to supersonic motions contain information on turbulent velocity field which is otherwise difficult to measure. However, the problem of separation of velocity and density fluctuations is far from being trivial. Using atomic hydrogen (HI) as a test case, I review techniques applicable to emission line studies with the emphasis on those that can provide information on the underlying power spectra of velocity and density. I show that recently developed mathematical machinery is promising for the purpose. Its application to HI shows that in cold neutral hydrogen the velocity fluctuations dominate the small scale structures observed in spectral-line data cubes and this result is very important for the interpretation of observational data, including the identification of clouds. Velocity fluctuations are shown to dominate the formation of small scale structures that can be erroneously identified as diffuse clouds. One may argue that the HI data is consistent with the Goldreich-Shridhar picture of magnetohydrodynamic turbulence, but the cascade from the scales of several kpc that this interpretation involves does not fit well in the current paradigm of energy injection. The issue whether magnetic field does make the turbulence anisotropic is still open, but if this is the case, I show that studies of emission lines can provide a reliable way of determining magnetic field direction. I discuss various techniques for studying interstellar turbulence using emission lines, e.g. spectral correlation functions, genus statistics and principal component analysis.