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3.2. Faraday Rotation 27
The RM can be expressed as:
∫ L[kpc]
RM [rad m −2 ] = 812 n e [cm −3 ]B z [µG] dz [kpc] , (3.2)
0
where n e is the electron gas density in the thermal plasma, B z is the magnetic field along the lineof-sight
and L is the integration path. Therefore the study of the Faraday effect across polarized
radio sources allows us to probe the magnetic field strength along the line-of-sight. As already
mentioned in Sec. 1.2.2, the polarization angle can be described by using the observables Stokes
parameters Q and U (Stokes 1852):
Ψ λ = 1 2 arctan (
Uλ
Q λ
)
, (3.3)
and it can be measured at several wavelengths by multi-frequency polarimetric radio observations.
Then, RM across radio sources can be derived through a linear fit of the observed polarization
angles as a function ofλ 2 (Eq. 3.1). As is well known, the determination of RM is complicated
because of the nπ ambiguities in the observedΨ obs .
Removal of these ambiguities requires
observations at least at three different wavelengths, well-spaced inλ 2 . An alternative is the method
of RM synthesis using simultaneous polarization observations over a contiguous frequency range,
which will be available with the new generation of wideband correlators (Brentjens & Bruyn
2005).
3.2.1 Internal Faraday Rotation
Internal RM occurs if thermal plasma and synchrotron emitting particles are mixed.
In this
case, together with the rotation of the polarization plane we observe a decrease of the degree of
polarization with increasing wavelength. Indeed, emission arising from different depths within a
source suffers differential Faraday rotation reducing the degree of polarization. The functional
form of the expected depolarization is in general related to the geometry of the source.
simplest modeling for such phenomenon is the optically-thin slab with uniform density and
magnetic field located entirely within the source. In this case, the degree of polarization is given
by (Burn 1966):
The
P Obs (λ)=P Int | sin(RM′ λ 2 )
RM ′ λ 2 |, (3.4)
where RM ′ is the internal Faraday RM and is equal to 1 2
of that expected for a foreground slab
screen of the same thermal density and field strength.
Even in the case of internal RM,λ 2 rotation holds at sufficiently short wavelengths.
particular, in the case of the slab model theλ 2 rotation is observed over 90 degrees then shows
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