Irregular magnetic fields and the far-infrared polarimetry of dust emission from interstellar clouds

The polarized thermal radiation at far-infrared and submillimeter wavelengths from dust grains in interstellar clouds with irregular magnetic fields is simulated. The goal is to determine to what degree irregularity in the magnetic fields can be consistent with the observation that the maps of the polarization vectors are relatively ordered. Detailed calculations are performed for the reduction in the fractional polarization and the dispersion in position angles as a function of the ratio of the irregular to the uniform magnetic field and as a function of the relevant dimensions measured in correlation lengths of the field. We show that the polarization properties of quiescent clouds and of star-forming regions are consistent with Kolmogorov-like turbulent magnetic fields that are comparable in magnitude to the uniform component of the magnetic fields. If the beam size is much smaller than the correlation length, L-corr, of the fields, the calculated percentage polarization, p, decreases to an asymptotic value when the number of correlation lengths, N-corr, through the cloud exceeds a few x 10. For these values of N-corr, the dispersion in the position angles, sigma(alpha), is still appreciable, decreasing to only similar to20degrees. However, when the finite size of a telescope beam is taken into account the asymptotic value of p is reached for fewer correlation lengths (smaller N-corr) because of averaging over the beam; sigma(alpha) becomes much smaller and is consistent with the observational data. The smoothing of the polarization properties due to the combined effect of the thickness of the cloud and the finite size of the beam can be described by a single variable that we designate as the generalized number of correlation lengths. In addition, we study various factors that may contribute to the decrease in the linear polarization percentage with increasing intensity that is observed at submillimeter and far-infrared wavelengths in many, although not all, dark clouds (the polarization hole'' effect). Depolarization due to a density cutoff in the polarizing effect of dust, thermalization, and correlations between the density and the properties of the magnetic field are considered.