Turbulence Spectra from Spectral Lines: Tests of the Velocity Channel Analysis and Velocity Coordinate Spectrum Techniques

Turbulence is a key element of the dynamics of astrophysical fluids, including those of interstellar medium, clusters of galaxies and circumstellar regions. Turbulent motions induce Doppler shifts of observable emission and absorption lines and this motivates studies of turbulence using precision spectroscopy. We provide high resolution numerical testing of the two promising techniques, namely, Velocity Channel Analysis and Velocity Coordinate Spectrum. We obtain an expression for the shot noise that the discretization of the numerical data entails and successfully test it. We show that numerical resolution required for recovering the underlying turbulent spectrum from observations depend on the spectral index of velocity fluctuations. Thus the low resolution testing may be misleading.