Polarization studies

Polarization is an intrinsic property of electromagnetic waves. EM-waves have two components which oscillate in the plane perpendicular to the direction of travel: a magnetic and an electric component that are perpendicular to one another. Polarization is the term which describes the direction of the EM-wave's transverse electric field. In general, the directions of these components are distributed randomly in a beam, the EM-wave is then called unpolarized. However, when one direction of oscillation is 'preferred' more above the rest, the wave is dubbed polarized and the amount of polarization is usually indicated in fractions of the total intensity.

Figure 2: The manifestation of three types of polarization

There are sources that can generate light waves which are partly polarized. It is also possible that an EM-wave comes in contact with a medium where it can get polarized or depolarized. By measuring the direction and strength of polarization at different frequencies and various positions on the source, we can get answers to questions about the manner of generation of waves, its neighbourhood, the foreground and about the orientation of the object. To specify and quantify the phase and polarization of radiation, there are a set of four parameters called the Stokes parameters. These observable quantities I, Q, U and V are operationally defined, but can be mathematically related to the electromagnetic field. Q and U together represent the linearly polarized component, with a 45 degree angle between them. V represents the circularly polarized component and I is a measure of the total power of the polarized radiation. With the use of these parameters, the polarization intensity and phase can be easily quantified.

Synchrotron radiation has a number of unique properties. One of them is that it generates highly polarized radiation dependent on the magnetic-field $\overrightarrow{B}$ of the surrounding area and these photons are emitted with energies ranging from infra-red to energetic X-rays. This is a great tool for astronomers studying active galaxies. Unfortunately, polarization studies require high resolution observations, because averaging of different rotations within the beam causes depolarization.

From the polarization properties of Quasars at different frequencies, one of the interesting things that can be studied is the foreground affecting it. Known as the Faraday effect, the plane of polarization of an electromagnetic wave can be rotated under the influence of a magnetic field (parallel to the direction of propagation) within the path of the observer.

Figure 3: Diagram of the Faraday effect

The amount of rotation $\beta$, displayed in figure (3), is given by RM $\cdot \lambda^{2}$, where $\lambda$ is the wavelength of the radiation and RM is a factor known as the rotation measure in units of radians $\cdot$ m$^{-2}$. RM depends on a number of parameters, see equation (1).

$$RM = \frac {e^{3}} {2\pi m^{2} c^{4}} \int_{0}^{d} n_{e} \overrightarrow{B} ds,$$ (1)

$\overrightarrow{B}$, the magnetic flux density in the direction of propagation

$n_{e}$, the number density of electrons

$d$, the length of the path where the light and magnetic field interact

$e$ and $m$, the charge and mass of an electron

$c$, the speed of light in a vacuum

Observing Faraday rotation in the radiation from RGs and Quasars are among the most important ways of studying the environment and foreground of these objects.