Velocity Anisotropy as a Diagnostic of the Magnetization of the Interstellar Medium and Molecular Clouds

We use a set of magnetohydrodynamic simulations of fully developed (driven) turbulence to study the anisotropy in the velocity field that is induced by the presence of the magnetic field. In our models, we study turbulence characterized by sonic Mach numbers M_s from 0.7 to 7.5 and Alfvén Mach numbers from 0.4 to 7.7. These are used to produce synthetic observations (centroid maps) that are then analyzed. To study the effect of large-scale density fluctuations and of white noise, we have modified the density fields and obtained new centroid maps, which are analyzed. We show that restricting the range of scales at which the anisotropy is measured makes the method robust against such fluctuations. We show that the anisotropy in the structure function of the maps reveals the direction of the magnetic field for M_A <~ 1.5, regardless of the sonic Mach number. We find that the degree of anisotropy can be used to determine the degree of magnetization (i.e., M_A ) for M_A <~ 1.5. To do this, one needs an additional measure of the sonic Mach number and an estimate of the line of sight magnetic field, both feasible by other techniques, offering a new opportunity to study the magnetization state of the interstellar medium.