Studying turbulence using Doppler-broadened lines: Velocity coordinate spectrum

We discuss a new technique for studying astrophysical turbulence that utilizes the statistics of Doppler-broadened spectral lines. The technique relates the power velocity coordinate spectrum (VCS), i. e., the spectrum of fluctuations measured along the velocity axis in position-position-velocity data cubes available from observations, to the underlying power spectra of the velocity/ density fluctuations. Unlike the standard spatial spectra, which are a function of angular wavenumber, the VCS is a function of the velocity wavenumber k(v) similar to 1/v. We show that absorption affects the VCS to a higher degree for small kv and obtain the criteria for disregarding the absorption effects for turbulence studies at large kv. We consider the retrieval of turbulence spectra from observations for high and low spatial resolution observations and find that the VCS allows one to study turbulence even when the emitting turbulent volume is not spatially resolved. This opens interesting prospects for using the technique for extragalactic research. We show that, while thermal broadening interferes with the turbulence studies using the VCS, it is possible to separate thermal and nonthermal contributions. This allows a new way of determining the temperature of the interstellar gas using emission and absorption spectral lines.