Faraday rotation and depolarization of synchrotron radio emission are considered in a consistent general approach, under conditions typical of spiral galaxies, i.e. when the magneto‐ionic medium and relativistic electrons are non‐uniformly distributed in a layer containing both regular and fluctuating components of magnetic field, thermal electron density and synchrotron emissivity. We demonstrate that non‐uniformity of the magneto‐ionic medium along the line of sight strongly affects the observable polarization patterns. The degree of polarization p and the observed Faraday rotation measure RM are very sensitive to whether or not the source is symmetric along the line of sight. The RM may change sign in a certain wavelength range in an asymmetric slab even when the line‐of‐sight magnetic field has no reversals. Faraday depolarization in a purely regular magnetic field can be much stronger than suggested by the low observed rotation measures. A twisted regular magnetic field may result in p increasing with λ— a behaviour detected in several galaxies.  We derive expressions for statistical fluctuations in complex polarization and show that random fluctuations in the degree of polarization caused by Faraday dispersion are expected to become significantly larger than the mean value of p at λ ≳ 20 − 30 cm. We also discuss depolarization arising from a gradient of Faraday rotation measure across the beam, both in the source and in an external Faraday screen. We briefly discuss applications of the above results to radio polarization observations.  We discuss how the degree of polarization is affected by the scaling of synchrotron emissivity ɛ with the total magnetic field strength B. We derive formulae for the complex polarization at λ → 0 under the assumption that ɛ ∝ B2B2⊥, which may arise under energy equipartition or pressure balance between cosmic rays and magnetic fields. The resulting degree of polarization is systematically larger than for the usually adopted scaling ɛ ∝ B2⊥; the difference may reach a factor of 1.5.

(Abridged) We use new multi-wavelength radio observations, made with the VLA and Effelsberg telescopes, to study the magnetic field of the nearby galaxy M51 on scales from $200\pc$ to several $\kpc$. Interferometric and single dish data are combined to obtain new maps at \wwav{3}{6} in total and polarized emission, and earlier \wav{20} data are re-reduced. We compare the spatial distribution of the radio emission with observations of the neutral gas, derive radio spectral index and Faraday depolarization maps, and model the large-scale variation in Faraday rotation in order to deduce the structure of the regular magnetic field. We find that the \wav{20} emission from the disc is severely depolarized and that a dominating fraction of the observed polarized emission at \wav{6} must be due to anisotropic small-scale magnetic fields. Taking this into account, we derive two components for the regular magnetic field in this galaxy: the disc is dominated by a combination of azimuthal modes, $m=0+2$, but in the halo only an $m=1$ mode is required to fit the observations. We disuss how the observed arm-interarm contrast in radio intensities can be reconciled with evidence for strong gas compression in the spiral shocks. The average arm--interam contrast, representative of the radii $r>2\kpc$ where the spiral arms are broader, is not compatible with straightforward compression: lower arm--interarm contrasts than expected may be due to resolution effects and \emph{decompression} of the magnetic field as it leaves the arms. We suggest a simple method to estimate the turbulent scale in the magneto-ionic medium from the dependence of the standard deviation of the observed Faraday rotation measure on resolution. We thus obtain an estimate of $50\pc$ for the size of the turbulent eddies.Comment: 21 pages, 18 figures (some at lower resolution than submitted version), accepted for publication in MNRA

Aims. We study the distribution of the molecular gas in the Andromeda galaxy (M 31) and compare this with the distributions of the atomic gas and the emission from cold dust at λ175 µm. Methods. We obtained a new 12 CO(J = 1−0)-line survey of the Andromeda galaxy with the highest resolution to date (23 , or 85 pc along the major axis), observed On-the-Fly with the IRAM 30-m telescope. We fully sampled an area of 2• × 0.• 5 with a velocity resolution of 2.6 km s −1 . In several selected regions we also observed the 12 CO(2−1)-line. Results. Emission from the 12 CO(1−0) line was detected from galactocentric radius R = 3 kpc to R = 16 kpc with a maximum in intensity at R ∼ 10 kpc. The molecular gas traced by the (velocity-integrated) (1−0)-line intensity is concentrated in narrow arm-like filaments, which often coincide with the dark dust lanes visible at optical wavelengths. Between R = 4 kpc and R = 12 kpc the brightest CO filaments define a two-armed spiral pattern that is described well by two logarithmic spirals with a pitch angle of 7• -8• .The arm-interarm brightness ratio averaged over a length of 15 kpc along the western arms reaches about 20 compared to 4 for H iat an angular resolution of 45 . For a constant conversion factor X CO , the molecular fraction of the neutral gas is enhanced in the spiral arms and decreases radially from 0.6 on the inner arms to 0.3 on the arms at R 10 kpc. The apparent gas-to-dust ratios N(H i)/I 175 and (N(H i) + 2N(H 2 ))/I 175 increase by a factor of ∼20 between the centre and R 14 kpc, whereas the ratio 2N(H 2 )/I 175 only increases by a factor of 4. Conclusions. Either the atomic and total gas-to-dust ratios increase by a factor of ∼20 or the dust becomes colder towards larger radii. A strong variation of X CO with radius seems unlikely. The observed gradients affect the cross-correlations between gas and dust. In the radial range R = 8-14 kpc total gas and cold dust are well correlated; molecular gas correlates better with cold dust than atomic gas. The mass of the molecular gas in M 31 within a radius of 18 kpc is M(H 2 ) = 3.6 × 10 8 M at the adopted distance of 780 kpc. This is 7% of the total neutral gas mass in M 31.

Context. Constraints on the origin and propagation of cosmic rays can be achieved by studying the variation in the spectral index of the synchrotron emission across external galaxies. Aims. We determine the variation in the nonthermal radio spectral index in the nearby spiral galaxy M 33 at a linear resolution of 360 pc. Methods. We separated the thermal and nonthermal components of the radio continuum emission without the assumption of a constant nonthermal spectral index. Using the Spitzer FIR data at 70 and 160 µm and a standard dust model, we dereddened the Hα emission. The extinction corrected Hα emission serves as a template for the thermal free-free radio emission. Subtracting this free-free emission from the observed 3.6 cm and 20 cm emission (Effelsberg and the VLA), we obtained the nonthermal maps. A constant electron temperature used to obtain the thermal radio intensity seems appropriate for M 33, which, unlike the Milky Way, has a shallow metallicity gradient. Results. For the first time, we derive the distribution of the nonthermal spectral index across a galaxy, M 33. We detect strong nonthermal emission from the spiral arms and starforming regions. Wavelet analysis shows that at 3.6 cm the nonthermal emission is dominated by contributions from starforming regions, while it is smoothly distributed at 20 cm. For the whole galaxy, we obtain thermal fractions of 51% and 18% at 3.6 cm and 20 cm, respectively. The thermal emission is slightly stronger in the southern than in the northern half of the galaxy. We find a clear radial gradient of mean extinction in the galactic plane. Conclusions. The nonthermal spectral index map indicates that the relativistic electrons suffer energy loss when diffusing from their origin in starforming regions towards interarm regions and the outer parts of the galaxy. We also conclude that the radio emission is mostly nonthermal at R > 5 kpc in M 33.

Abstract. The configuration of the regular magnetic field in M 31 is deduced from radio polarization observations at the wavelengths λλ6, 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 −19• to p −8• . 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 th 1 kpc. Faraday effects offer a powerful method to detect thick magneto-ionic disks or halos around spiral galaxies.