The configuration of the regular magnetic field in M 31 is deduced from radio polarization observations at the wavelengths \lambda \lambda 6 , 11 and 20 { cm } .
By fitting the observed azimuthal distribution of polarization angles , we find that the regular magnetic field , averaged over scales 1–3 kpc , is almost perfectly axisymmetric in the radial range 8 to 14 { kpc } , and follows a spiral pattern with pitch angles of p \simeq - 19 \degr to p \simeq - 8 \degr .
In the ring between 6 and 8 { kpc } a perturbation of the dominant axisymmetric mode may be present , having the azimuthal wave number m = 2 .
A systematic analysis of the observed depolarization allows us to identify the main mechanism for wavelength dependent depolarization – Faraday rotation measure gradients arising in a magneto-ionic screen above the synchrotron disk .
Modelling of the depolarization leads to constraints on the relative scale heights of the thermal and synchrotron emitting layers in M 31 ; the thermal layer is found to be up to three times thicker than the synchrotron disk .
The regular magnetic field must be coherent over a vertical scale at least similar to the scale height of the thermal layer , estimated to be h _ { \mathrm { th } } \simeq 1 { kpc } .
Faraday effects offer a powerful method to detect thick magneto-ionic disks or halosaround spiral galaxies .