Astrophysical magnetic fields and nonlinear dynamo theory

▪ Abstract 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 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...

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Galactic Magnetism: Recent developments and perspectives

A variety of observations suggest that magnetic fields are present in all galaxies and galaxy clusters. These fields are characterized by a modest strength ${(10}^{\ensuremath{-}7}\char21{}{10}^{\ensuremath{-}5}\mathrm{G})$ and huge spatial scale $(\ensuremath{\lesssim}1\mathrm{Mpc}).$ It is generally assumed that magnetic fields in spiral galaxies arise from the combined action of differential rotation and helical turbulence, a process known as the \ensuremath{\alpha}\ensuremath{\omega} dynamo. However, fundamental questions concerning the nature of the dynamo as well as the origin of the seed fields necessary to prime it remain unclear. Moreover, the standard \ensuremath{\alpha}\ensuremath{\omega} dynamo does not explain the existence of magnetic fields in elliptical galaxies and clusters. The author summarizes what is known observationally about magnetic fields in galaxies, clusters, superclusters, and beyond. He then reviews the standard dynamo paradigm, the challenges that have been leveled against it, and several alternative scenarios. He concludes with a discussion of astrophysical and early-Universe candidates for seed fields.

https://arxiv.org/pdf/astro-ph/0207240.pdf

Origin of galactic and extragalactic magnetic fields

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

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Current Status of Turbulent Dynamo Theory. From Large-Scale to Small-Scale Dynamos

We present a simple semi-analytical model of non-linear, mean field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the 'no-z' approximation to a non-linear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where non-linear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g. due to the galactic fountain or wind) and the other, arising from anisotropy of turbulence as suggested by Vishniac & Cho. We argue that the latter is significant if the galactic differential rotation is strong enough: in our model, for R ω ≤ -10 in terms of the corresponding turbulent magnetic Reynolds number. We confirm that the intensity of gas outflow from the galactic disc optimal for the dynamo action is close to that expected for normal spiral galaxies. The steady-state strength of the large-scale magnetic field supported by the helicity advection is still weaker than that corresponding to equipartition with the turbulent energy. However, the Vishniac-Cho helicity flux can boost magnetic field further to achieve energy equipartition with turbulence. For stronger outflows that may occur in starburst galaxies, the Vishniac-Cho flux can be essential for the dynamo action. However, this mechanism requires a large-scale magnetic field of at least ≃1 μG to be launched, so that it has to be preceded by a conventional dynamo assisted by the advection of magnetic helicity by the fountain or wind.

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Galactic dynamos supported by magnetic helicity fluxes

A steady density wave in a disc-like galaxy could lead to a spiral form for the crucial α-effect term in standard dynamo theory. We had earlier studied this problem under the thin-disc approximation and by effecting an approximate separation of variables between the z-dependence and the r, φ-dependences of the magnetic field. We return to this problem by making an alternative approximation of our equations, which allows a better treatment of the case of strong departures from axisymmetry, albeit with a cruder treatment of the z-dependence. The numerical solution of the equations reveals, as in our earlier work, the existence of rapidly growing, global, bisymmetric magnetic modes, corotating with the density wave

L. Mestel

Papers

Galactic dynamos and density wave theory – II. An alternative treatment for strong non-axisymmetry