Statistical Tracing of Magnetic Fields: Comparing and Improving the Techniques

Magnetohydrodynamic turbulence displays velocity anisotropies that reflect the direction of the magnetic field. This anisotropy has led to the development of a number of statistical techniques for studying magnetic fields in the interstellar medium. In this paper, we review and compare three techniques that use radio position-position-velocity data to determine magnetic field strength and morphology: the correlation function anisotropy (CFA), principal component analysis of anisotropies (PCAA), and the more recent velocity gradient technique (VGT). We compare these three techniques and suggest improvements to the CFA and PCAA techniques to increase their accuracy and versatility. In particular, we suggest and successfully implement a much faster way to calculate nonperiodic correlation functions for the CFA. We discuss possible improvements to the current implementation of the PCAA. We show the advantages of the VGT in terms of magnetic field tracing and stress the complementary nature with the other two techniques.