The dynamics of the interstellar medium (ISM) are strongly affected by turbulence, which shows increased anisotropy in the presence of a magnetic field. We expand upon the Esquivel & Lazarian method to estimate the Alfven Mach number using the struct
ure function anisotropy in velocity centroid data from position-position-velocity maps. We utilize 3D magnetohydrodynamic (MHD) simulations of fully developed turbulence, with a large range of sonic and Alfvenic Mach numbers, to produce synthetic observations of velocity centroids with observational characteristics such as thermal broadening, cloud boundaries, noise, and radiative transfer effects of carbon monoxide. In addition, we investigate how the resulting anisotropy-Alfven Mach number dependency found in Esquivel & Lazarian (2011) might change when taking the second moment of the position-position-velocity cube or when using different expressions to calculate the velocity centroids. We find that the degree of anisotropy is related primarily to the magnetic field strength (i.e. Alfven Mach number) and the line-of-sight orientation, with a secondary effect on sonic Mach number. If the line-of-sight is parallel to up to ~45 deg off of the mean field direction, the velocity centroid anisotropy is not prominent enough to distinguish different Alfvenic regimes. The observed anisotropy is not strongly affected by including radiative transfer, although future studies should include additional tests for opacity effects. These results open up the possibility of studying the magnetic nature of the ISM using statistical methods in addition to existing observational techniques.
The interstellar medium of the Milky Way is multi-phase, magnetized and turbulent. Turbulence in the interstellar medium produces a global cascade of random gas motions, spanning scales ranging from 100 parsecs to 1000 kilometres. Fundamental paramet
ers of interstellar turbulence such as the sonic Mach number (the speed of sound) have been difficult to determine because observations have lacked the sensitivity and resolution to directly image the small-scale structure associated with turbulent motion. Observations of linear polarization and Faraday rotation in radio emission from the Milky Way have identified unusual polarized structures that often have no counterparts in the total radiation intensity or at other wavelengths, and whose physical significance has been unclear. Here we report that the gradient of the Stokes vector (Q,U), where Q and U are parameters describing the polarization state of radiation, provides an image of magnetized turbulence in diffuse ionized gas, manifested as a complex filamentary web of discontinuities in gas density and magnetic field. Through comparison with simulations, we demonstrate that turbulence in the warm ionized medium has a relatively low sonic Mach number, M_s <~ 2. The development of statistical tools for the analysis of polarization gradients will allow accurate determinations of the Mach number, Reynolds number and magnetic field strength in interstellar turbulence over a wide range of conditions.
