Propagation-induced circular polarization in synchrotron sources

Malcolm Kennett, Don Melrose, PASA, 15 (2), 211
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Title/Abstract Page: Propagation-induced circular polarization in
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Elliptically polarized natural modes

The natural wave modes of a gas of highly relativistic particles are close to linearly polarized for nearly all angles of propagation and for frequencies typical of synchrotron emission by these highly relativistic particles (Sazonov 1969; Melrose 1997a). Hence, as the synchrotron radiation propagates through the source it experiences generalized Faraday rotation due to the contribution of the highly relativistic particles to the polarization of the natural modes of the ambient plasma. The actual properties of the natural wave modes in a synchrotron source depend on contributions from both the cold plasma and from the highly relativistic particles. In general the modes are elliptically polarized with the ellipticity determined by the ratio of the number densities of cold and highly relativistic particles. The wave modes are nearly circular if the cold plasma dominates and nearly linear if the relativistic particles dominate.

In some sources it may be that the relativistic particles are electron-positron pairs (e.g., Wilson & Weiler 1997). Electrons and positrons contribute with the same sign to the linearly polarized component and with the opposite sign to the circularly polarized component. If the distributions of electrons and positrons are the same the wave modes can have no circular component and, more importantly, the intrinsic circular polarization from the synchrotron radiation sums to zero. Hence, the alternative mechanism proposed here can produce some circular polarization from an electron-positron pair plasma, despite the fact that the intrinsic circular polarization is zero in this case.

An important qualitative point in the following discussion is that the orientation of the magnetic field projected onto the plane of the sky must vary along the line of sight through the source for generalized Faraday rotation to occur (cf. Hodge 1982). If this were not the case, the polarization point for the emitting synchrotron radiation would lie on the axis defined by the two natural modes and would not change along the ray path. Thus, for example, generalized Faraday rotation in the near half of the source could partially convert the linear polarization of radiation from the far half of the source into circular polarization provided that the orientation of the magnetic field in the two halves is significantly different.

The relative phase difference between the two natural modes determines the angle through which the polarization point rotates, cf. Figure 3. This relative phase, tex2html_wrap_inline494 say, depends on the difference, tex2html_wrap_inline406, in wavenumber between the two modes, and the distance, L, across the source region where the relativistic particles are present. If tex2html_wrap_inline500 is very small, then the difference between the natural modes has no significant effect, and the polarization of the radiation escaping from the source region is the intrinsic polarization determined by the synchrotron emission alone. In the opposite limit, when tex2html_wrap_inline500 is very large, the polarization point rotates many times about the axis. This case corresponds to the two natural modes propagating independently of each other. The net polarization in this case may be found by separating the emission into the two natural modes before integrating over the source. The intermediate case tex2html_wrap_inline504 allows substantial conversion of linear into circular polarization, but the cyclic nature of the change then implies that the polarization of the escaping radiation would be a strong function of tex2html_wrap_inline500. In particular, because tex2html_wrap_inline500 is a strong function of frequency, tex2html_wrap_inline374 would also be a strong function of frequency. Moreover, any variation in tex2html_wrap_inline500 across the beamwidth of the telescope would reduce the observable circular polarization.

These properties suggest that significant circular polarization might arise as a propagation effect under a variety of different conditions in a synchrotron source. Two specific examples are the following:

  1. The relativistic particles dominate, so that the natural modes are linearly polarized; one could then explain a measured value of tex2html_wrap_inline374 either due to tex2html_wrap_inline504 (producing a substantial circular polarization) over a small fraction (tex2html_wrap_inline518) of the source, or by tex2html_wrap_inline520 over a substantial fraction of the source.
  2. The admixture of relativistic particles and cold plasma causes the natural modes to have a small circular component, and one has tex2html_wrap_inline522 across the source. This case has already been discussed by Pacholczyk (1973) and is considered only briefly here.

We discuss these two possibilities in the next section.

Next Section: Relativistic rotation measure (RRM)
Title/Abstract Page: Propagation-induced circular polarization in
Previous Section: Generalized Faraday rotation
Contents Page: Volume 15, Number 2

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