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We study possibility of obtaining velocity spectra by studying turbulence inan optically thick medium using velocity centroids (VCs).We find that theregime of universal, i.e. independent of underlying turbulence statistics,fluctuations discovered originally within the velocity channel analysis (VCA)carries over to the statistics of VCs. In other words, for large absorptionsthe VC lose their ability to reflect the spectra of turbulence. Combining ourpresent study with the earlier studies of centroids in Esquivel & Lazarian, weconclude that centroids are applicable for studies subsonic/transsonicturbulence for the range of scales that is limited by the absorption effects.We also consider VCs based on absorption lines and define the range of theirapplicability. We address the problem of analytical description of spectra andanisotropies of fluctuations that are available through studies using VC. Weobtain spectra and anisotropy of VC fluctuations arising from Alfv\'en, slowand fast modes that constitute the compressible MHD cascade to address theissue of anisotropy of VC statistics, and show how the VC anisotropy can beused to find the media magnetization as well as to identify and separatecontributions from Alfv\'en, slow and fast modes. Our study demonstrates thatVCs are complementary to the tools provided by the VCA. In order to studyturbulent volume for which the resolution of single dish telescopes isinsufficient, we demonstrate how the studies of anisotropy can be performedusing interferometers.

Study of velocity centroids based on the theory of fluctuations in position-position-velocity space