Statistics of velocity centroids: effects of density-velocity correlations and non-Gaussianity

We continue with our previous work on statistics of velocity centroids, to retrieve information about the scaling properties of an underlying turbulent velocity field from spectroscopic observations. We use synthetic data sets with extreme effects of velocity-density correlations that we create artificially, which also have a non-Gaussian distribution of fluctuations. We confirm that centroids can be used to obtain the scaling properties of the turbulent velocity when the ratio of the density dispersion to the mean density is less than unity, regardless of velocity-density correlations and non-Gaussianity. It was found that extreme velocity-density correlations can distort the statistics of velocity centroids, impeding the recovery of the turbulent velocity spectral index from centroids. We show that such correlations introduce high-order moments to the maps of centroids, which we disregarded in previous work, but that they are only important when the density dispersion is large in comparison with the mean density. It was also found that non-Gaussian velocity and/or density distort the statistics of centroids too, but to a lower degree than extreme cross-correlations.