We discuss current observational and theoretical knowledge of magnetic fields, especially the large-scale structure in the disks and halos of spiral galaxies. Among other topics, we consider the enhancement of global magnetic fields in the interarm regions, magnetic spiral arms, and representations as superpositions of azimuthal modes, emphasizing a number of unresolved questions. It is argued that a turbulent hydromagnetic dynamo of some kind and an inverse cascade 1 Now at Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, United Kingdom. 155 0066-4146/96/0915-0155$08.00 156 BECK ET AL of magnetic energy gives the most plausible explanation for the regular galactic magnetic fields. Primordial theory is found to be unsatisfactory, and fields of cosmological origin may not even be able to provide a seed field for a dynamo. Although dynamo theory has its own problems, the general form of the dynamo equations appears quite robust. Finally, detailed models of magnetic field generation in galaxies, allowing for factors such as spiral structure, starbursts, galactic winds, and fountains, are discussed and confronted with observations.

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.

Aims. In the context of models of galaxy formation and evolution, we investigate the cosmological evolution of large-and small-scale magnetic fields inside galaxies. Methods. We use the dynamo theory to derive the timescales of amplification and ordering of magnetic fields in disk and puffy galaxies. Turbulence in protogalactic halos generated by thermal virialization can drive an efficient turbulent dynamo. Results from simulations of hierarchical structure formation cosmology provide a tool to develop an evolutionary model of regular magnetic fields coupled with galaxy formation and evolution. Results. The turbulent (small-scale) dynamo was able to amplify a weak seed magnetic field in halos of protogalaxies to a few μG strength within a few 10 8 yr. This turbulent field served as a seed to the mean-field (large-scale) dynamo. Galaxies similar to the Milky Way formed their disks at z ≈ 10 and regular fields of μG strength and a few kpc coherence length were generated within 2 Gyr (at z ≈ 3), but field-ordering on the coherence scale of the galaxy size required an additional 6 Gyr (at z ≈ 0.5). Giant galaxies formed their disks at z ≈ 10, allowing more efficient dynamo generation of strong regular fields (with kpc coherence length) already at z ≈ 4. However, the age of the Universe is short for fully coherent fields in giant galaxies larger than 15 kpc to have been achieved. Dwarf galaxies should have hosted fully coherent fields at z ≈ 1. After a major merger, the strength of the turbulent field is enhanced by a factor of a few. Conclusions. This evolutionary scenario can be tested by measurements of polarized synchrotron emission and Faraday rotation with the planned Square Kilometre Array (SKA). We predict an anticorrelation between galaxy size and ratio between ordering scale and galaxy size. Weak regular fields (small Faraday rotation) in galaxies at z < ∼ 3 are signatures of major mergers. Undisturbed dwarf galaxies should host fully coherent fields, giving rise to strong Faraday rotation signals. Radio observations may serve as a clock for measuring the time since the last major merger.

Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.Comment: 4 pages, 2 figures, accepted by A&A Letter

Aims. Although the time of the Maunder minimum (1645-1715) is widely known as a period of extremely low solar activity, it is still being debated whether solar activity during that period might have been moderate or even higher than the current solar cycle #24. We have revisited all existing evidence and datasets, both direct and indirect, to assess the level of solar activity during the Maunder minimum. Methods. We discuss the East Asian naked-eye sunspot observations, the telescopic solar observations, the fraction of sunspot active days, the latitudinal extent of sunspot positions, auroral sightings at high latitudes, cosmogenic radionuclide data as well as solar eclipse observations for that period. We also consider peculiar features of the Sun (very strong hemispheric asymmetry of the sunspot location, unusual differential rotation and the lack of the K-corona) that imply a special mode of solar activity during the Maunder minimum.Results. The level of solar activity during the Maunder minimum is reassessed on the basis of all available datasets. Conclusions. We conclude that solar activity was indeed at an exceptionally low level during the Maunder minimum. Although the exact level is still unclear, it was definitely lower than during the Dalton minimum of around 1800 and significantly below that of the current solar cycle #24. Claims of a moderate-to-high level of solar activity during the Maunder minimum are rejected with a high confidence level.

Various approaches to estimate turbulent transport coefficients from numerical simulations of hydromagnetic turbulence are discussed. A quantitative comparison between the averaged magnetic field obtained from a specific three-dimensional simulation of a rotating turbulent shear flow in a slab and a simple one-dimensional alpha-omega dynamo model is given. A direct determination of transport coefficients is attempted by calculating the correlation matrix of different components of the field and its derivatives. This matrix relates the electromotive force to physically relevant parameters like the tensor components of the -effect and the turbulent diffusivity. The -effect operating on the toroidal field is found to be negative and of similar magnitude as the value obtained in previous work by correlating the electromotive force with the mean magnetic field. The turbulent diffusion of the toroidal field is comparable to the kinematic viscosity that was determined earlier by comparing the stress with the shear. However, the turbulent diffusion of the radial field component is smaller and can even be formally negative. The method is then modified to obtain the spectral dependence of the turbulent transport coefficients on the wavenumber. There is evidence for nonlocal behaviour in that most of the response comes from the smallest wavenumbers corresponding to the largest scale possible in the simulation. Again, the turbulent diffusion coefficient for the radial field component is small, or even negative, which is considered unphysical. However, when the diffusion tensor is assumed to be diagonal the radial component of the diffusion tensor is positive, supporting thus the relevance of a nonlocal approach. Finally, model calculations are presented using nonlocal prescriptions of the -effect and the turbulent diffusion. We emphasize that in all cases the electromotive force exhibits a strong stochastic component which make the -effect and the turbulent diffusion intrinsically noisy.

Coherent structures in the distribution of the Faraday rotation measure (RM) of extragalactic radio sources are isolated using wavelet transformation techniques. A new algorithm of wavelet analysis for data points non‐uniformly distributed on a sphere is developed and implemented. Signatures of the magnetic fields in the local (Orion) arm, the Sagittarius arm (and its extension, the Carina arm), the synchrotron Loop I and, possibly, the Perseus arm have been revealed using the RM catalogues of Simard‐Normandin et al. (551 sources) and Broten et al. (663 sources). Unlike earlier analyses of the RM sky, our approach has allowed us to assess the stability of the results with respect to modifications of the data sample. Only the aforementioned features remain stable under mild sample modifications. We consider separately low‐latitude sources at |b|<10° and, using the model of electron density distribution of Cordes et al., we estimate magnetic field strength by comparing the model wavelet transform with that of the real data. Independent estimates of the mean magnetic field strength in the Orion arm using low‐ and high‐latitude sources converge to 1.4±0.3 μG. Rotation measures of low‐latitude sources provide a clear indication of a magnetic field reversal at a distance 0.6–1 kpc towards the Galactic Centre. Our analysis has revealed for the first time the extension of the reversal in the Carina arm. Low‐latitude sources from the catalogue of Broten et al. indicate a magneto‐ionic structure in the direction of the Perseus arm with the magnetic field direction reversed with respect to that in the Orion arm. The extent of the region with reversed magnetic field near the Sun is 3 kpc or more in the azimuthal direction. The average pitch angle of magnetic field in the nearby spiral arms is 15°, and the mean field strength in the Sagittarius–Carina and Perseus arms is 1.7±0.3 μG and 1.4±1.2 μG, respectively. The line‐of‐sight magnetic field in Loop I is estimated as 0.9±0.3 μG. We find firm evidence of a dominant even symmetry of the local mean magnetic field with respect to the Galactic equator. Our results are compatible with a moderate large‐scale north–south asymmetry, with the magnetic field in the southern hemisphere being stronger in a region of at least 3 kpc in size. It cannot be excluded, however, that the asymmetry is local and results from vertical bending of magnetic lines in a region of about 400 pc in size, with the Sun being located close to the top of a magnetic loop, the magnetic field of which is 0.5 μG stronger than the average field.

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