Constraining dynamo theories of magnetic field origin by observation is indispensable but challenging, in part because the basic quantities measured by observers and predicted by modelers are different. We clarify these differences and sketch out ways to bridge the divide. Based on archival and previously unpublished data, we then compile various important properties of galactic magnetic fields for nearby spiral galaxies. We consistently compute strengths of total, ordered, and regular fields, pitch angles of ordered and regular fields, and we summarize the present knowledge on azimuthal modes, field parities, and the properties of non-axisymmetric spiral features called magnetic arms. We review related aspects of dynamo theory, with a focus on mean-field models and their predictions for large-scale magnetic fields in galactic discs and halos. Further, we measure the velocity dispersion of H I gas in arm and inter-arm regions in three galaxies, M 51, M 74, and NGC 6946, since spiral modulation of the root-mean-square turbulent speed has been proposed as a driver of non-axisymmetry in large-scale dynamos. We find no evidence for such a modulation and place upper limits on its strength, helping to narrow down the list of mechanisms to explain magnetic arms. Successes and remaining challenges of dynamo models with respect to explaining observations are briefly summarized, and possible strategies are suggested. With new instruments like the Square Kilometre Array (SKA), large data sets of magnetic and non-magnetic properties from thousands of galaxies will become available, to be compared with theory.

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We compare various models and approximations for non-linear mean-field dynamos in disc galaxies to assess their applicability and accuracy, and thus to suggest a set of simple solutions suitable to model the large-scale galactic magnetic fields in various contexts. The dynamo saturation mechanisms considered are the magnetic helicity balance involving helicity fluxes (the dynamical α-quenching) and an algebraic αquenching. The non-linear solutions are then compared with the marginal kinematic and asymptotic solutions. We also discuss the accuracy of the no-z approximation. Although these tools are very different in the degree of approximation and hence complexity, they all lead to remarkably similar solutions for the mean magnetic field. In particular, we show that the algebraic α-quenching non-linearity can be obtained from a more physical dynamical α-quenching model in the limit of nearly azimuthal magnetic field. This suggests, for instance, that earlier results on galactic disc dynamos based on the simple algebraic non-linearity are likely to be reliable, and that estimates based on simple, even linear models are often a good starting point. We suggest improved no-z and algebraic α-quenching models, and also incorporate galactic outflows into a simple analytical dynamo model to show that the outflow can produce leading magnetic spirals near the disc surface. The simple dynamo models developed are applied to estimate the magnetic pitch angle and the arm-interarm contrast in the saturated magnetic field strength for realistic parameter values.

We study the cosmic evolution of the magnetic fields of a large sample of spiral galaxies in a cosmologically representative volume by employing a semi-analytic galaxy formation model and numerical dynamo solver in tandem. We start by deriving timeand radius-dependent galaxy properties using the galform galaxy formation model, which are then fed into the nonlinear mean-field dynamo equations. These are solved to give the large-scale (mean) field as a function of time and galactocentric radius for a thin disc, assuming axial symmetry. A simple prescription for the evolution of the small-scale (random) magnetic field component is also adopted. We find that, while most massive galaxies are predicted to have large-scale magnetic fields at redshift z = 0, a significant fraction of them is expected to contain negligible large-scale field. Our model indicates that, for most of the galaxies containing large-scale magnetic fields today, the mean-field dynamo becomes active at z < 3. Moreover, the typical magnetic field strength at any given galactic stellar mass is predicted to decline with time up until the present epoch, in agreement with our earlier results. We compute the radial profiles of pitch angle, and find broad agreement with observational data for nearby galaxies.