  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 structure 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.
