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 (ne). 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 / m2 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.
Figure 3. Faraday rotation measures between 6.2 cm and 11.1 cm at 5' resolution, computed in regions where the polarized intensities at both wavelengths are larger than 5× the rms noise (Berkhuijsen et al., in prep.)
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 ne2 and thus mainly traces peaks in thermal density (HII regions), RM traces the diffuse, extended component of ne. The RM amplitude is 77 rad / m2. With a regular field strength of 4 µG, the average electron density ne 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).