Dispersion Of Position Angles Research Articles

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, Lcorr, of the fields, the calculated percentage polarization, p, decreases to an asymptotic value when the number of correlation lengths, Ncorr, through the cloud exceeds a few × 10. For these values of Ncorr, the dispersion in the position angles, σα, is still appreciable, decreasing to only ~20°. 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 Ncorr) because of averaging over the beam; σα 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.

Irregular Magnetic Fields in Interstellar Clouds and the Linear Polarization of Starlight

Calculations are performed for the linear polarization of starlight due to extinction by aligned dust grains when the starlight traverses a medium with irregular magnetic fields. This medium is intended to represent the optically thick components of interstellar clouds which are observed to make little, if any, contribution to the polarization of starlight. In agreement with the observations, we find that the polarization properties of the starlight---the average fractional polarization and the dispersion in position angles---can be essentially unchanged. For this, the rms of the irregular component must be greater than the average magnetic field, which in turn tends to imply that the turbulent velocities in these interstellar clouds are super-Alfvenic.

The Distribution of Fractional Linear Polarization and the Random Component of Polarization Position Angle

One of the most fascinating features of the polarization of pulsar radio emission is the occurrence of orthogonal modes of polarization. The origin of the modes is not clear, but, whatever their underlying nature, the modes will affect observables such as the instantaneous linear polarization. We derive an idealized distribution of fractional linear polarization assuming that the modes are superposed and compare our result with observations. We discuss how superposed modes may affect the position angle distributions.Consider a subpulse composed of superposed modes of orthogonal polarization. We assume that each mode is completely linearly-polarized with no dispersion in position angle. If the flux densities of the individual modes are represented by the independent random variablesX1andX2, then the linear polarization of the subpulse is related toX=X1−X2and its total intensity isY=X1+X2. We denote the means of the mode distributions byμ1andμ2and their standard deviations byσ1andσ2. The means are generally not the same because observed distributions of position angle (e.g. Stinebring et al. 1984) show that the modes generally do not occur with equal frequency. If the individual modes are normally-distributed with identical standard deviations,XandYare also normally-distributed, independent random variables. In this ideal case, the distribution of fractional polarization,Z=|X/Y|, is