Magnetic Field Diagnostics Based on Far‐Infrared Polarimetry: Tests Using Numerical Simulations

The dynamical state of star-forming molecular clouds cannot be understoodwithout determining the structure and strength of their magnetic fields.Measurements of polarized far-infrared radiation from thermally aligned dustgrains are used to map the orientation of the field and estimate its strength,but the accuracy of the results has remained in doubt. In order to assess thereliability of this method, we apply it to simulated far-infrared polarizationmaps derived from three-dimensional simulations of supersonicmagnetohydrodynamical turbulence, and compare the estimated values to the knownmagnetic field strengths in the simulations. We investigate the effects oflimited telescope resolution and self-gravity on the structure of the maps.Limited observational resolution affects the field structure such that smallscale variations can be completely suppressed, thus giving the impression of avery homogeneous field. The Chandrasekhar-Fermi method of estimating the meanmagnetic field in a turbulent medium is tested, and we suggest an extension tomeasure the rms field. Both methods yield results within a factor of 2 forfield strengths typical of molecular clouds, with the modified versionreturning more reliable estimates for slightly weaker fields. However, neithermethod alone works well for very weak fields, missing them by a factor of up to150. Taking the geometric mean of both methods estimates even the weakestfields accurately within a factor of 2.5. Limited telescope resolution leads toa systematic overestimation of the field strengths for all methods. We discussthe effects responsible for this overestimation and show how to extractinformation on the underlying (turbulent) power spectrum.Comment: 30 pages, 15 figures (figs 1, 4, 5 reduced quality), submitted to ApJ Hires version of figs 1, 4, 5 see ftp://ftp.mpia-hd.mpg.de/pub/heitsch/HZM00/hiresfigs.tar.g