Statistics of Velocity Centroids: Effects of Correlations of Density and Velocity.

Centroids of velocity from spectroscopic observations have been widely used to study the properties of the underlying turbulent field, however, it was not clear until recently how density fluctuations affect the results. In a previous work, Lazarian and Esquivel provided an analytical description of velocity centroids. In that work the structure function of centroids was decomposed into four contributions: column density, integrated velocity, ``cross-terms'', and density-velocity ``cross-correlations''. From the second term (integrated velocity) we can retrieve the spectral index of velocity. At the same time, the contribution of column density, entirely attainable from observations, can in principle be removed. In this poster, we present an in-depth analysis of the remaining terms. It is found that the ratio of the standard deviation to the mean of density correlates with the ``cross-term''. We also introduce artificial density-velocity ``cross-correlations''. And, for a reasonable level of those, it is found that when velocity centroid fails to trace velocity the ``cross-term'' contaminates the velocity statistics well before the ``cross-correlation'' term. Our results suggest that limitations of the use of centroids to study the scaling properties of velocity will arise primarily from the ``cross-terms''.