Faraday rotation and depolarization of synchrotron radio emission are
considered in a consistent general approach, under conditions typical
of spiral galaxies, i.e. when the magneto-ionic medium and relativisti
c electrons are non-uniformly distributed in a layer containing both r
egular and fluctuating components of magnetic field, thermal electron
density and synchrotron emissivity, We demonstrate that non-uniformity
of the magneto-ionic medium along the line of sight strongly affects
the observable polarization patterns. The degree of polarization p and
the observed Faraday rotation measure RM are very sensitive to whethe
r or not the source is symmetric along the line of sight. The RM may c
hange sign in a certain wavelength range in an asymmetric slab even wh
en the line-of-sight magnetic field has no reversals. Faraday depolari
zation in a purely regular magnetic field can be much stronger than su
ggested by the low observed rotation measures, A twisted regular magne
tic field may result in p increasing with lambda - a behaviour detecte
d in several galaxies. We derive expressions for statistical fluctuati
ons in complex polarization and show that random fluctuations in the d
egree of polarization caused by Faraday dispersion are expected to bec
ome significantly larger than the mean value of p at lambda greater th
an or similar to 20-30cm, We also discuss depolarization arising from
a gradient of Faraday rotation measure across the beam, both in the so
urce and in an external Faraday screen. We briefly discuss application
s of the above results to radio polarization observations. We discuss
how the degree of polarization is affected by the scaling of synchrotr
on emissivity epsilon with the total magnetic field strength B, We der
ive formulae for the complex polarization at lambda --> 0 under the as
sumption that epsilon alpha (BBperpendicular to2)-B-2, which may arise
under energy equipartition or pressure balance between cosmic rays an
d magnetic fields. The resulting degree of polarization is systematica
lly larger than for the usually adopted scaling epsilon alpha B-perpen
dicular to(2); the difference may reach a factor of 1.5.