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Three deep radio continuum surveys of the Andromeda galaxy, M 31, wereperformed at 11.3, 6.2, and 3.6 cm wavelength with the Effelsberg 100-mtelescope. At all wavelengths, the total and polarized emission is concentratedin a ring-like structure between about 7 kpc and 13 kpc radius from the center.Propagation of cosmic rays away from star-forming regions is evident. The ringof synchrotron emission is wider than the ring of the thermal radio emission,and the radial scale length of synchrotron emission is larger than that ofthermal emission. The polarized intensity from the ring variesdouble-periodically with azimuthal angle, indicating that the ordered magneticfield is almost oriented along the ring, with a pitch angle of -14{\deg} $\pm$2{\deg}. Faraday rotation measures (RM) show a large-scale sinusoidal variationwith azimuthal angle, signature of an axisymmetric spiral (ASS) regularmagnetic field, plus a superimposed double-periodic variation of a bisymmetricspiral (BSS) field with about 6x smaller amplitude. The dominating ASS field ofM 31 is the most compelling case so far of a field generated by the action of amean-field dynamo. The RM amplitude between 6.2 cm and 3.6 cm is about 50%larger than between 11.3 cm and 6.2 cm, indicating that Faraday depolarizationat 11.3 cm is stronger than at 6.2 cm and 3.6 cm. The phase of the sinusoidalRM variation of -7{\deg} $\pm$ 1{\deg} is interpreted as the average spiralpitch angle of the regular field. The average pitch angle of the ordered field,as derived from the intrinsic orientation of the polarized emission (correctedfor Faraday rotation), is significantly smaller: -26{\deg} $\pm$ 3{\deg}. Thedifference in pitch angle of the regular and the ordered fields indicates thatthe ordered field contains a significant fraction of an anisotropic turbulentfield that has a different pattern than the regular (ASS + BSS) field.

Magnetic fields and cosmic rays in M 31. I. Spectral indices, scale lengths, Faraday rotation, and magnetic field pattern