Velocity Centroids as Tracers of the Turbulent Velocity Statistics

We use the results of magnetohydrodynamic (MHD) simulations to emulate spectroscopic observations and produce maps with variations of velocity centroids to study their scaling properties. In order to assess under which circumstances the scaling properties of the velocity field can be retrieved from velocity centroids, we compare two point statistics of velocity centroids with those of the underlying velocity field and analytic predictions presented in a previous paper (Lazarian & Esquivel 2003). We tested successfully a criterion for recovering velocity statistics from velocity centroids derived in our previous work. We propose an approximation of the early criterion using only the variances of “unnormalized” velocity centroids and column density maps. If the criteria are satisfied then the structure function of velocity centroids is dominated by the structure function of velocity. We show that ordinary velocity centroids (normalized and unnormalized) trace the velocity statistics in subsonic and mildly supersonic turbulence (e. g. Mach numbers . 2.5). At the same time, for highly supersonic turbulence, the statistics of ordinary centroids are strongly affected by density fluctuations, and thus fail to trace the statistics of velocity. We have confirmed for a Mach number ∼ 7 that “modified” velocity centroids (introduced in our earlier work) were able to trace the velocity statistics. This is achieved by subtracting a term that has an important contribution of density fluctuations and can be entirely obtained from observations. Subject headings: ISM: general — ISM: structure — MHD — radio lines: ISM — turbulence