**3.3. Rotation measures**

Faraday rotation measures (*RMs*) are proportional to the component of
the regular field *along* the line of sight and to the density of
thermal electrons (*n*_{e}). In case of a toroidal regular
field, | *RM* | is maximum on the major axis and zero on the minor
axis; *RM*
varies sinusoidally with azimuthal angle. If the regular field is of
axisymmetric spiral type (ASS), the variation of *RM* with azimuthal
angle is phase-shifted by an angle equal to the pitch angle of the
magnetic spiral.

Figure 3 shows the *RMs* in the M31 ring,
derived from the Effelsberg data at
6 cm and
11 cm at 5'
resolution. The average *RM* of about
-90 rad / *m*^{2} is due to the foreground medium in the
Galaxy. The azimuthal
variation between 8 and 12 kpc radius can be fitted by a sine wave,
the signature of an axisymmetric (ASS) field as expected from dynamo
models (Shukurov, this volume). A detailed analysis of all available
polarization data including, those at
20 cm, is given by
Fletcher et al. (this volume). The large-scale pattern in the *RM* map
is the proof that the field in M31 is not only regular, but also
*coherent*
as it preserves its direction all over the galaxy. The radial component of
the field points *towards the center of M31* everywhere.

The *RM* distribution in Fig. 3 is much
smoother than that of the thermal emission at the same resolution. While
the latter is sensitive to
*n*_{e}^{2} and thus mainly traces peaks in thermal
density (HII regions), *RM* traces the diffuse, extended
component of *n*_{e}. The *RM* amplitude is
77 rad / *m*^{2}. With a regular
field strength of 4 *µ*G, the average electron density
*n*_{e} is
0.015 cm^{-3} over
a pathlength of 3 kpc.
The true extent of the diffuse thermal gas in M31 in unknown
(Sect. 4).