ar X iv : a st ro - p h / 04 08 17 6 v 1 1 0 A ug 2 00 4 Obtaining Statistics of Turbulent Velocity from Astrophysical Spectral Line Data

Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent velocities. We discuss Velocity-Channel Analysis (VCA) and its offspring Velocity Coordinate Spectrum (VCS) that are based on the analytical description of the spectral line statistics. Those techniques are well suited for studies of supersonic turbulence. We stress that a great advantage of VCS is that it does not necessary require good spatial resolution. Addressing the studies of mildly supersonic and subsonic turbulence we discuss the criterion that allows to determine whether a traditional tool for such a research, namely, Velocity Centroids are dominated by density or velocity. We briefly discuss the use of higher order correlations as the means to study intermittency of turbulence. We discuss observational data available and prospects of the field. 1. What can be learned from fluctuations of velocity? As a rule astrophysical fluids are turbulent and the turbulence is magnetized. This ubiquitous turbulence determines the transport properties of interstellar medium many properties of Solar and stellar winds, accretion disks etc. One may say that to understand heat conduction, transport and acceleration of cosmic rays, propagation of electromagnetic radiation in different astrophysical environments it is absolutely essential to understand the properties of underlying turbulence. The mysterious processes of star formation (see McKee & Tan 2002, Elmegreen 2002, Pudritz 2001) and interstellar chemistry (see Falgarone 1999 and references therein), shattering and coagulation of dust (see Lazarian & Yan 2003 and references therein) are also intimately related to properties of magnetized compressible turbulence (see reviews by Elmegreen & Scalo 2004). From the point of view of fluid mechanics astrophysical turbulence is characterized by huge Reynolds numbers, Re, which is the inverse ratio of the eddy turnover time of a parcel of gas to the time required for