Technique for separating velocity and density contributions in spectroscopic data and its application to studying turbulence and magnetic fields

Based on the theoretical description of Position-Position-Velocity(PPV) statistics in Lazarian & Pogosyan(2000), we introduce a new technique called the Velocity Decomposition Algorithm(VDA) in separating the PPV fluctuations arising from velocity and density fluctuations. Using MHD turbulence simulations, we demonstrate its promise in retrieving the velocity fluctuations from PPV cube in various physical conditions and its prospects in accurately tracing the magnetic field. We find that for localized clouds, the velocity fluctuations are most prominent at the wing part of the spectral line, and they dominate the density fluctuations. The same velocity dominance applies to extended HI regions undergoing galactic rotation. Our numerical experiment demonstrates that velocity channels arising from the cold phase of atomic hydrogen (HI) are still affected by velocity fluctuations at small scales. We apply the VDA to HI GALFA-DR2 data corresponding to the high-velocity cloud HVC186+19-114 and high latitude galactic diffuse HI data. Our study confirms the crucial role of velocity fluctuations in explaining why linear structures are observed within PPV cubes. We discuss the implications of VDA for both magnetic field studies and predicting polarized galactic emission that acts as the foreground for the Cosmic Microwave Background studies. Additionally, we address the controversy related to the filamentary nature of the HI channel maps and explain the importance of velocity fluctuations in the formation of structures in PPV data cubes. VDA will allow astronomers to obtain velocity fluctuations from almost every piece of spectroscopic PPV data and allow direct investigations of the turbulent velocity field in observations.