4.3. Magnetic field shape in Andromeda (M31) and other galaxies
An optical study of the magnetic field in M31 made by Martin & Shawl (1982) indicated a magnetic field aligned roughly in the plane of the disk, with more or less azimuthal field lines and along the spiral arms.
Only the first method, the Faraday rotation one, can give the magnetic field shape and direction. It does so through the variation of the position angle of maximum polarization value as a function of observed wavelength.
Figure 14 shows the run of the magnetic field B as a function of the galactic radius, in the Andromeda galaxy (= M31). Negative magnetic field values (opposite sense or direction, by convention) are not seen, implying no magnetic field reversal with increasing galactic radii.
Figure 14. The run of the magnetic field value as a function of the galactic radius rgal, in the Andromeda (M31) galaxy. The observed total magnetic field values (dashes), the uniform component values (open circles), and the random component values (dots) are shown.
As mentioned in Section 3.7.1, early solutions of the linear dynamo equations were done by splitting the dynamo equations into 3 independent axes. As mentioned in Section 3.5.1, observations of the global magnetism in nearby spiral galaxies have shown two shapes: ASS or BSS.
In M31, the azimuthal mode mazim in the -axis is the lowest (mazim = 0), i.e., the magnetic field is axisymmetric. In M31, the vertical mode p in the z-axis is the lowest (p = 0), i.e., the magnetic field is symmetric above and below the galactic plane. In M31, the radial mode n along the r-axis is the lowest (n = 0), i.e., there is no magnetic field reversal with radius. This radial mode n of the magnetic field is determined by the behavior of the combined radial potential (r), and (r) rises rapidly at a radius of 7 kpc (Fig. 4 in Ruzmaikin et al., 1985), contrary to the slow rise of (r) in the Milky Way (Fig. 3 in Vallée, 1991b). So in M31 the ranges of dynamo solutions for the n modes start at the same inner radial boundary, not at different radii, and therefore the lowest n mode dominates (n = 0, no magnetic field reversal).