Interstellar cloud structure: The statistics of centroid velocities

Abstract

Context. The statistical properties of maps of line centroids have been used for almost 50 years, but there is still no general agreement on their interpretation. Aims. We have tried to quantify which properties of underlying turbulent velocity fields can be derived from centroid velocity maps, and we tested conditions under which the scaling behaviour of the centroid velocities matches the scaling of the three-dimensional velocity field. Methods. Using fractal cloud models we systematically studied the relation between three-dimensional density and velocity fields and the statistical properties of the resulting line centroid maps. We paid special attention to cases with large density fluctuations resembling supersonic interstellar turbulence. Starting from the Δ-variance analysis, we derived a new tool to compute the scaling behaviour of the three-dimensional velocity field from observed intensity and centroid velocity maps. Results. We provide two criteria to decide whether the information from the centroid velocities directly reflects the properties of the underlying velocity field. Applying these criteria allows us to understand the different results found so far in the literature for interpreting the statistics of velocity centroids. The new iteration scheme can be used to derive the three-dimensional velocity scaling from centroid velocity maps for arbitrary density and velocity fields, but it requires accurate knowledge of the average density of the interstellar cloud under consideration. © ESO 2006.