# Centroids velocity studies

The observation of molecular lines from interstellar clouds provides a basic clue to measure their velocity structure. The scaling behaviour of the statistical velocity fluctuations allows to draw conclusions on the sources of energy input, dissipation, and the processes governing the transfer of energy along the turbulent cascade. Although the statistical properties of maps of line centroids have been studied for almost 50 years now, there is still no agreement which properties of the underlying turbulent velocity field can be derived from these maps. Recent systematic studies gave contradicting results. Miville-Deschenes et al. (2003) claimed that the centroid scaling matches the true velocity scaling, Ossenkopf & Mac Low (2002) inferred that the spectral index of the centroids is reduced by one compared to the velocity index, and Brunt & Mac Low (2004) concluded that this relation is a function of the Mach number of the turbulence.

Using fractal cloud models studied systematically the relation between three-dimensional density and velocity fields and the statistical properties of the produced line centroid maps. It turned out that we can explain all previous results from the literature within a unified scheme depending on the relative contribution of density and velocity fluctuations.

Delta-variance spectra of weighted centroid velocities for an fBm density structure with Beta=2.6 and an average density of 0.25 times the density dispersion and a fBm velocity structure with Beta=3.7. The dash-dot line demonstrates the reconstruction of the underlying velocity scaling from the centroid map by the developed iteration scheme. |

We have shown that the Delta-variance analysis is an appropriate tool to characterise the scaling properties of both velocity centroid maps and the underlying three-dimensional velocity field. We provide two criteria to decide whether the information from the centroid velocities directly reflects the properties of the underlying velocity field. The most accurate criterion is a small ratio between the density dispersion and the mean density. Without knowing the average density in the considered medium we can use a second criterion, first derived by Lazarian & Esquivel (2003) and extended by Ossenkopf et al (2005a), requiring that the Delta-variance of the velocity centroids at a given scale weighted by the sqare of the average intensity is larger than the Delta-variance of the integrated intensity map at the same scale weighted by the average velocity variance.

In all cases where the criteria for a velocity-dominated centroid spectrum are not fulfilled there is a transition to density-contaminated spectra which are systematically shallower. For this general case we developed a sophisticated iteration scheme to derive the velocity structure from the centroid maps. Unfortunately, the accurate determination of the power spectrum of the velocity fluctuations depends on an accurate knowledge of the average density, a condition that is not easy to fulfil for observed interstellar clouds.

Contact: Volker Ossenkopf