Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1972
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972ap%26ss..19...25s&link_type=abstract
Astrophysics and Space Science, Volume 19, Issue 1, pp.25-45
Astronomy and Astrophysics
Astrophysics
4
Scientific paper
The degree of circular polarizationp c is calculated for two models of a source of synchrotron radiation:
(1)
A source with an inhomogeneous magnetic field and isotropic angular distribution of the electrons with respect to the magnetic field;
(2)
A source with a homogeneous magnetic field and anisotropic angular distribution of the electrons in which the anisotropy of angular distribution substantially increases with the electron energy. The first model can be used to describe extended radio-sources; and the second, to describe compact radio-sources. For those sources, whose observed polarization properties correspond to the first model, we obtain an integral equation which connects the observed distribution of the sources with the extent of their linear and circular polarization (p l andp c ) and the unknown distribution of the sources over the strengthB and the degree of homogeneity ɛ=(B 0/B)2 of the magnetic field;B 0 is a homogenous field,B 0≪B. A solution of the integral equation obtained is found for a particular case. This solution makes it possible to determine the distribution of different types of sources over ɛ if the distribution of these sources in the extent of linear polarization is known. The formulae obtained make it possible to indicate which sources with a known degree of linear polarization should be expected to exhibit highest circular polarization. In the discussion of the first model the question is raised as to the information one can get about the magnetic field by using observations of both linear and circular polarization for a separate source, and for a number of sources. It is shown that the determination of the most probable values ofB and ɛ in a separate source based on the known values ofp l andp c for the source, is possible only if one knows the distribution overB and ɛ of the sources of the type to which the source in question belongs. The observational data now available make it possible to find the distribution of the sources only over ɛ. Since the distribution overB and ɛ is at present unknown, even a very strong upper limit forp c in the case of a separate source does not enable us to give an exact upper limit for the strength of the magnetic field in this source. In the first model the upper limit for the magnetic field can be obtained only if the upper limit ofp c is known for a certain number of sourcesN, withN≫1. This limit allows for much stronger fields than are usually admitted. This last fact should be taken into consideration when one deals with the results of observations of circular polarization in sources with strong magnetic fields. The first model presents some difficulties when we compare it with observations of some compact sources. The second model can explain why one observes in these sources a violation of the lawp c ˜v -1/2 and a change of sign inp c when the frequency of the observationsv changes.
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