Statistics of Velocity from Spectral Data: Modified Velocity Centroids

We address the problem of studying interstellar turbulence using spectral line data. We find a criterion when the velocity centroids may provide trustworthy velocity statistics. To enhance the scope of centroids applications, we construct a measure that we term “modified velocity centroids” (MVCs) and derive an analytical solution that relates the 2D spectra of the modified centroids with the underlying 3D velocity spectrum. We test our results using synthetic maps constructed with data obtained through simulations of compressible magnetohydrodynamical (MHD) turbulence. We show that the modified velocity centroids (MVCs) are complementary to the the Velocity Channel Analysis (VCA) technique. Employed together, they make determining of the velocity spectral index more reliable and for wider variety of astrophysical situations. Subject headings: turbulence – ISM: general, structure – MHD – radio lines: ISM.