Annu. Rev. Astron. Astrophys. 1996. 34:
155206 Copyright © 1996 by . All rights reserved 
2.2. LargeScale Field Patterns
The plane of polarization of a linearly polarized radio wave rotates when the wave passes through a plasma with a regular magnetic field. The rotation angle increases with the integral of n_{e} B_{} along the line of sight (where n_{e} is the thermal electron density and B_{} is the component of the total magnetic field along the line of sight) and with ^{2} (where is the wavelength of observation). The quantity / ^{2} is called the rotation measure, RM. The observed RM is sensitive to the regular magnetic field _{} because the random fields B_{} mostly cancel. The sign of RM allows the two opposite directions of _{} to be distinguished. An accurate determination of RM requires observations at (at least) three wavelengths because the observed orientation of the polarization plane is ambiguous by a multiple of ± 180° (see Ruzmaikin & Sokoloff 1979). Unlike equipartition estimates, which are insensitive to the presence of field reversals within the volume observed by the telescope beam, the observed value of Faraday rotation will decrease with increasing number of reversals.
Although the filled apertures of singledish telescopes are sensitive to all spatial structures above the resolution limit, synthesis instruments such as the VLA cannot provide interferometric data at short spacings. This shortcoming results in some blindness to extended emission. Missing largescale structures in maps of Stokes parameters Q and U can systematically distort the polarization angles and hence the RM distribution, so that the inclusion of additional data from singledish telescopes in all Stokes parameters is required. In Section 3.4 (Figure 3) we show the result of such a successful combination by using a maximumentropy method.
A convenient general way to parameterize the global magnetic field (irrespective of its origin) is by Fourier decomposition in terms of the azimuthal angle measured in the plane of the galaxy, = _{m} _{m} exp(i m ). In practice, observations are analyzed within rings (centered at the galaxy's center) whose width is chosen to be consistent with the resolution of the observations. The result is a set of Fourier coefficients of the largescale magnetic field for each ring. Usually, a combination of m = 0 and m = 1 modes is enough to provide a statistically satisfactory fit to the data. This is a remarkable indication of the presence of genuine global magnetic structures in spiral galaxies.
All observed magnetic fields have significant radial and azimuthal components: The magnetic lines of the regular field are spirals (Section 8.3). We distinguish between spiral structures that can be considered as basically axisymmetric (ASS), and basically antisymmetric or bisymmetric (BSS), with respect to rotation by 180°. Note that higher azimuthal Fourier modes are expected to be superimposed on these dominant ones, but these should have relatively small amplitudes. Fields containing several Fourier components of significant amplitude have mixed spiral structure (MSS); this might be considered to be a combination of ASS and BSS.
A further classification of magnetic structures according to their symmetry with respect to the galaxy's midplane distinguishes symmetric S (i.e. even parity or quadrupole) from antisymmetric (odd parity or dipole) modes A.
Mixedparity distributions (M), in which the magnetic fields are neither even nor odd but are superpositions, are also possible. This notation is supplemented with a value of the azimuthal wave number m, e.g. S0 means a quadrupole axisymmetric field. The notation used in discussions of global magnetic structures in spiral galaxies in presented in Table 1.
Vertical  Azimuthal structure  

structure  ASS  BSS  MSS 
 
Even  S0  S1  S0 + S1 
Odd  A0  A1  A0 + A1 
Mixed  M0  M1  M0 + M1 

An ASS (BSS) field produces a 2periodic (periodic) distribution of RM along (Sofue et al 1986, Krause 1990, Wielebinski & Krause 1993). For the m = 0 mode, the phase of the variation of RM with is equal to the magnetic pitch angle, p = arctan(_{r} / _{}). Using the observed azimuthal distribution of RM in a galaxy, the structure of the lineofsight component of a largescale magnetic field can be studied. This method is difficult to apply if the data suffer from Faraday depolarization, if the regular field is not parallel to the plane of the galaxy, if its pitch angle in the disk is not constant, or if the disk is surrounded by a halo with magnetic fields of comparable strengths.
A more direct method of analysis considers polarization angles without converting them into Faraday rotation measures (Ruzmaikin et al 1990;, Sokoloff et al 1992; EM Berkhuijsen et al, in preparation) There are three main contributions to the observed polarization angle: = _{0} + RM ^{2} + RM_{fg} ^{2}, where _{0} is determined by the transverse magnetic field in the galaxy, RM is associated with Faraday rotation by the lineofsight magnetic field in the galaxy, and RM_{fg} is the foreground rotation measure. Thus, a direct analysis of patterns at several wavelengths allows a selfconsistent study of all three components of the regular magnetic field. Another advantage of this method is that complicated magnetic structures along the line of sight can be studied. Implementations of this method employ consistent statistical tests such as the ^{2} and Fisher criteria, thereby allowing the reliability of the results to be assessed.
Note that Faraday rotation analysis yields an average value, <n_{e}B_{}>. Information on _{} can be extracted only if a reliable model for the distribution of n_{e} is available, which is often not the case. If, for example, the thermal gas has a low filling factor, any result concerning _{} may not be representative.