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Extending Velocity Channel Analysis for Studying Turbulence Anisotropies

We extend the velocity channel analysis (VCA), introduced by Lazarian & Pogosyan, of the intensity fluctuations in the velocity slices of position-position-velocity (PPV) spectroscopic data from Doppler broadened lines to study statistical anisotropy of the underlying velocity and density that arises in a turbulent medium from the presence of magnetic field. In particular, we study analytically how the anisotropy of the intensity correlation in the channel maps changes with the thickness of velocity channels. In agreement with the earlier VCA studies we find that the anisotropy in the thick channels reflects the anisotropy of the density field, while the relative contribution of density and velocity fluctuations to the thin velocity channels depends on the density spectral slope. We show that the anisotropies arising from Alfven, slow and fast magnetohydrodynamical modes are different, in particular, the anisotropy in PPV created by fast modes is opposite to that created by Alfven and slow modes, and this can be used to separate their contributions. We successfully compare our results with the recent numerical study of the PPV anisotropies measured with synthetic observations. We also extend our study to the medium with self-absorption as well as to the case of absorption lines. In addition, we demonstrate how the studies of anisotropy can be performed using interferometers.