A Stochastic Theory for the Wavelength Dependence of Linear Polarization of Radio Sources.

Abstract

The following model is proposed: The source contains n elementary radiators or cells of equal power output which have perfect linear polarization independent of frequency. Some cells m have identical polarization angles, while the remaining n-m cells have polarization angles which are independent random variables with a uniform probability density function over the range 0 to 2ir. Between each cell and the observer is a medium which produces Faraday rotation of the polarization angles. The Faraday rotations are independent Gaussian random variables with a standard deviation of R rad/m2. The fractional polarization is the expected value of the sum of the polarization vectors divided by n, and is given by the formula u(N) = [(2n)-'+m(m- 1)n-0 exp(-R2N4)j1, where N is the wavelength in meters. The model fits the observations of many radio galaxies and quasi-stellar sources including 3C33, MSH 23-64, 3C196, and Her A; but it fails to fit the observations of Cyg A and Tan A. The source Cyg A has an increase in fractional polarization with wavelength near 1 cm, but the model can give only constant or decreasing fractional polarization with wavelength. Extensions of the model which could describe Cyg A and Tan A seem feasible. The average rotation measure of the source (a measurable quantity) is independent of the fractional polarization in the present theory. Burn and Sciama (Monthly Not~ces Roy. Astron. Soc. 133, 5,1966) have described a theory based on a Fourier transform relation between the fractional polarization and a function which distributes the radiated power with Faraday depth. (At a certain Faraday depth, the number of rotations to the observer is constant.) The Burn and Sciama theory requires that the average polarization angle of each Faraday depth is identical, but no such assumption is required in the present theory.