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 centroid applications, we construct a measure that we term modified velocity centroids (MVCs) and derive an analytical solution that relates the two-dimensional spectra of the modified centroids with the underlying three-dimensional velocity spectrum. We test our results using synthetic maps constructed with data obtained through simulations of compressible MHD turbulence. We show that the MVCs are complementary to the Velocity Channel Analysis technique. Employed together, they make the determination of the velocity spectral index more reliable for a wider variety of astrophysical situations.