Numerical experiments with a simple nonlinear mean-field dynamo model

Rädler, K.-H.; Wiedemann, E.

doi:10.1080/03091928908243464

Cited by 18 publications

(5 citation statements)

References 7 publications

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“…If only axisymmetric solutions are permitted, the S0 solution would be a stable end state (Brandenburg et al 1989). However, as was shown by Rädler & Wiedemann (1989), this is an artefact of the restriction to axisymmetry. Fully non-axisymmetric models demonstrate that the stellar surface field can undergo extended transients via a non-axisymmetric mode before the axisymmetric dipole solution is restored.…”

Section: Stellar Surface Magnetic Field Structurementioning

confidence: 87%

Advances in mean-field dynamo theory and applications to astrophysical turbulence

Brandenburg

2018

J. Plasma Phys.

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Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies, and the early Universe are discussed. We focus particularly on aspects of spatio-temporal nonlocality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and timescales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modeling this regime may be related to shortcomings in modelling solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking. † Email address for correspondence: brandenb@nordita.org † In the following, we continue using the lowercase symbols u and b instead of U ′ and B ′ to denote fluctuations of U and B.

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Section: Stellar Surface Magnetic Field Structurementioning

confidence: 87%

Advances in mean-field dynamo theory and applications to astrophysical turbulence

Brandenburg

2018

J. Plasma Phys.

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“…The fact that Im Γ = 0 for the anti-symmetric mode at R αh 10 appears to be an artefact of including only a small number of the free-decay modes into the perturbation series. The series (59) converges rather slowly (Rädler & Wiedemann 1989;Rädler et al 1990) and adding a few more terms does not always improve the accuracy (Sokoloff et al 2008). Therefore, the model for the halo magnetic field that involves only a modest number of modes can reproduce only relatively simple magnetic configurations (and yet quite non-trivial -see Fig.…”

Section: Basic Magnetic Structuresmentioning

confidence: 99%

A physical approach to modelling large-scale galactic magnetic fields

Shukurov

Rodrigues

Bushby

et al. 2019

A&A

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Context.A convenient representation of the structure of the large-scale galactic magnetic field is required for the interpretation of polarization data in the sub-mm and radio ranges, in both the Milky Way and external galaxies. Aims. We develop a simple and flexible approach to construct parametrised models of the large-scale magnetic field of the Milky Way and other disc galaxies, based on physically justifiable models of magnetic field structure. The resulting models are designed to be optimised against available observational data. Methods. Representations for the large-scale magnetic fields in the flared disc and spherical halo of a disc galaxy were obtained in the form of series expansions whose coefficients can be calculated from observable or theoretically known galactic properties. The functional basis for the expansions is derived as eigenfunctions of the mean-field dynamo equation or of the vectorial magnetic diffusion equation.Results. The solutions presented are axially symmetric but the approach can be extended straightforwardly to non-axisymmetric cases. The magnetic fields are solenoidal by construction, can be helical, and are parametrised in terms of observable properties of the host object, such as the rotation curve and the shape of the gaseous disc. The magnetic field in the disc can have a prescribed number of field reversals at any specified radii. Both the disc and halo magnetic fields can separately have either dipolar or quadrupolar symmetry. The model is implemented as a publicly available software package galmag which allows, in particular, the computation of the synchrotron emission and Faraday rotation produced by the model's magnetic field. Conclusions. The model can be used in interpretations of observations of magnetic fields in the Milky Way and other spiral galaxies, in particular as a prior in Bayesian analyses. It can also be used for a simple simulation of a time-dependent magnetic field generated by dynamo action.

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“…An efficient technique [43] to find the critical value of the dynamo number, D c for a given α(r, z) is to solve the dynamo equations for a sufficiently large (supercritical) R α with a modified form of the coefficient, α(r, z), that depends on |B| (so that the field is eventually driven to a steady state) but has the same spatial form as α(r, z) at all times:…”

Section: For Details]mentioning

confidence: 99%

The Origin of Large-Scale Magnetic Fields in Low-Mass Galaxies

2019

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The origin of large-scale magnetic fields, detected in some low-mass (dwarf and irregular) galaxies via polarised synchrotron emission and Faraday rotation, remained unexplained for a long time. We suggest that mean-field dynamo can be active in galaxies of this class despite their slow rotation because their discs are relatively thick. Earlier assessments of the possibility of the mean-field dynamo action in low-mass galaxies relied on estimates applicable to thin discs, such as those in massive spiral galaxies. Using both order-of-magnitude estimates and numerical solutions, we show that the strength of differential rotation required to amplify magnetic field reduces as the aspect ratio of the galactic gas layer increases. Thus, the puzzle of the origin of large-scale magnetic fields appears to be solved. As a result, this class of galaxies provides a new ground for testing our understanding of galactic magnetism.

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Numerical experiments with a simple nonlinear mean-field dynamo model

Cited by 18 publications

References 7 publications

Advances in mean-field dynamo theory and applications to astrophysical turbulence

Advances in mean-field dynamo theory and applications to astrophysical turbulence

A physical approach to modelling large-scale galactic magnetic fields

The Origin of Large-Scale Magnetic Fields in Low-Mass Galaxies

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