On the Measurement of the Magnitude and Orientation of the Magnetic Field in Molecular Clouds

We demonstrate that the combination of Zeeman, polarimetry, and ion-to-neutral molecular line width ratio measurements permits the determination of the magnitude and orientation of the magnetic field in the weakly ionized parts of molecular clouds. Zeeman measurements provide the strength of the magnetic field along the line of sight, polarimetry measurements give the field orientation in the plane of the sky, and the ion-to-neutral molecular line width ratio determines the angle between the magnetic field and the line of sight. We apply the technique to the M17 star-forming region using a HERTZ 350 μm polarimetry map and HCO+-to-HCN molecular line width ratios to provide the first three-dimensional view of the magnetic field in M17.