Magnetic fields and cosmic rays in M 31. I. Spectral indices, scale
  lengths, Faraday rotation, and magnetic field pattern
  Three deep radio continuum surveys of the Andromeda galaxy, M 31, were
performed at 11.3, 6.2, and 3.6 cm wavelength with the Effelsberg 100-m
telescope. At all wavelengths, the total and polarized emission is concentrated
in 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 ring
of synchrotron emission is wider than the ring of the thermal radio emission,
and the radial scale length of synchrotron emission is larger than that of
thermal emission. The polarized intensity from the ring varies
double-periodically with azimuthal angle, indicating that the ordered magnetic
field 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 variation
with azimuthal angle, signature of an axisymmetric spiral (ASS) regular
magnetic field, plus a superimposed double-periodic variation of a bisymmetric
spiral (BSS) field with about 6x smaller amplitude. The dominating ASS field of
M 31 is the most compelling case so far of a field generated by the action of a
mean-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 depolarization
at 11.3 cm is stronger than at 6.2 cm and 3.6 cm. The phase of the sinusoidal
RM variation of -7{\deg} $\pm$ 1{\deg} is interpreted as the average spiral
pitch angle of the regular field. The average pitch angle of the ordered field,
as derived from the intrinsic orientation of the polarized emission (corrected
for Faraday rotation), is significantly smaller: -26{\deg} $\pm$ 3{\deg}. The
difference in pitch angle of the regular and the ordered fields indicates that
the ordered field contains a significant fraction of an anisotropic turbulent
field that has a different pattern than the regular (ASS + BSS) field.
