We present λ3.5 cm and λ6.2 cm radio continuum maps in total and polarized intensity of the barred galaxies NGC 1097 (at 2 -15 resolution) and NGC 1365 (at 9 -25 resolution). A previously unknown radio galaxy southwest of NGC 1097 is reported. Apart from a smooth faint envelope and a bright central region, both galaxies exhibit radio ridges roughly overlapping with the massive dust lanes in the bar region. The contrast in total intensity across the radio ridges is compatible with compression and shear of an isotropic random magnetic field, where the gas density compression ratio is approximately equal to 4 and the cosmic ray density is constant across the ridges. The contrast in polarized intensity is significantly smaller than that expected from compression and shearing of the regular magnetic field; this could be the result of decoupling of the regular field from the dense molecular clouds. The regular field in the ridge is probably strong enough to reduce significantly shear in the diffuse gas (to which it is coupled) and hence to reduce magnetic field amplification by shearing. This contributes to the misalignment of the observed field orientation with respect to the velocity vectors of the dense gas. Our observations, for the first time, indicate that magnetic forces can control the flow of the diffuse interstellar gas at kiloparsec scales. The total radio intensity reaches its maximum in the circumnuclear starburst regions, where the equipartition field strength is about 60 µG, amongst the strongest fields detected in spiral galaxies so far. The regular field in the inner region has a spiral shape with large pitch angle, indicating the action of a dynamo. Magnetic stress leads to mass inflow towards the centre, sufficient to feed the active nucleus in NGC 1097. -We detected diffuse X-ray emission, possibly forming a halo of hot gas around NGC 1097.

Abstract. Faraday rotation of the polarization plane in magnetized thermal plasma provides one of the most efficient methods to deduce regular magnetic fields from radio astronomical observations. Since the Faraday rotation measure RM is proportional to an integral, along the line of sight, of magnetic field weighted with thermal electron density, RM is believed to yield the regular magnetic field averaged over large volume. Here we show that this is not the case in a turbulent medium where fluctuations in magnetic field and electron density are not statistically independent, and so contribute to RM. For example, in the case of pressure equilibrium, magnetic field can be anticorrelated with plasma density to produce a negative contribution. As a result, the strength of the regular magnetic field obtained from RM can be underestimated if the fluctuations in electron density and magnetic field are neglected. The anticorrelation also reduces the standard deviation of RM. We further discuss the effect of the positive correlations where the standard treatment of RM leads to an overestimated magnetic field. Because of the anisotropy of the turbulent magnetic field, the regular magnetic fields strength, obtained from synchrotron emission using standard formulae, can be overestimated. A positive correlation between cosmic-ray number density and magnetic field leads to an overestimate of the strengths of the regular and total fields. These effects can explain the difference between the strengths of the regular Galactic magnetic field as indicated by RM and synchrotron emissivity data and reconcile the magnetic field strength in the Solar vicinity with typical strength of regular magnetic fields in external galaxies.

Abstract. We consider the magnetic helicity balance for the galactic dynamo in the framework of the local dynamo problem, as well as in the no-z model (which includes explicitly the radial distribution of the magnetic fields). When calculating the magnetic helicity balance we take into account the redistribution of the small-scale and large-scale magnetic fields between the magnetic helicities, as well as magnetic helicity transport and diffusion due to smallscale turbulence. We demonstrate that the magnetic helicity flux through the galactic disc boundaries leads to a steady-state magnetic field with magnetic energy comparable to the equipartition energy of the turbulent motions of the interstellar medium. If such flux is ignored, the steady-state magnetic field is found to be much smaller than the equipartition field. The total magnetic helicity flux through the boundaries consists of both an advective flux and a diffusive flux. The exact ratio of these contributions seems not to be crucial for determining the strength of the steady-state magnetic field and its structure. However at least some diffusive contribution is needed to smooth the magnetic helicity profile near to the disc boundaries. The roles of various transport coefficients for magnetic helicity are investigated, and the values which lead to magnetic field configurations comparable with those observed are determined.

A shell model of magnetohydrodynamic turbulence, which allows one to conserve all the integrals of motion in both two and three dimensions, is proposed and studied. We demonstrate that this model reproduces basic facts known in the small-scale turbulent dynamo theory. In particular, we consider a process of redistribution of magnetic helicity generated by the mean-field dynamo, described in the model as magnetic forcing, into a small-scale magnetic field. We argue that the resulting equilibrium magnetic field spectrum strongly depends on the level of magnetic helicity and cross helicity, introduced by the large scales. The spectra with spectral index ''Ϫ5/3'' dominate if the cross helicity vanishes. If the level of cross helicity is high ͑correlated velocity and magnetic field͒ the spectra depend on the magnetic helicity: the strong magnetic helicity suppresses any cascade providing steep spectra, while the vanishing helicity of turbulent magnetic fields results in the occurrence of Kraichnan-Iroshnikov spectral index ''Ϫ3/2.'' ͓S1063-651X͑98͒04103-8͔

Abstract.We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic α-quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstrate behaviour comparable with the observed phenomenology, provided that a suitable set of governing dynamo parameters is chosen. On the other hand, the observational data are shown to be rich enough to reject some other sets of governing parameters. We conclude that, in spite of the very preliminary state of the observations and the crude nature of the model, the idea of using observational data to constrain our ideas concerning magnetic field generation in the framework of the solar dynamo appears promising.