The Generation of Cosmic Magnetic Fields

Rädler, K.-H.

doi:10.1007/3-540-45371-7_3

Cited by 25 publications

(26 citation statements)

References 84 publications

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“…As the magnetic field is divergence-free, its three component can be represented by two scalar potentials, S and T (Chandrasekhar 1961;Rädler 2000):…”

Section: Structure Of the Magnetic Fieldmentioning

confidence: 99%

Temperature distribution in magnetized neutron star crusts

Geppert¹,

Küker

Page

2006

A&A

101

124

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We continue the study of the effects of a strong magnetic field on the temperature distribution in the crust of a magnetized neutron star (NS) and its impact on the observable surface temperature. Extending the approach initiated in Geppert et al. (2004), we consider more complex and, hence, more realistic, magnetic field structures but still restrict ourselves to axisymmetric configurations. We put special emphasis on the heat blanketing effect of a toroidal field component. We show that asymmetric temperature distributions can occur and a crustal field consisting of dipolar poloidal and toroidal components will cause one polar spot to be larger than the opposing one. These two warm regions can be separated by an extended cold equatorial belt. As an example we present an internal magnetic field structure which can explain, assuming local blackbody emission, both the X-ray and optical spectra of the isolated NS RXJ 1856-3754, the hot polar regions dominating the X-ray flux and the equatorial belt contributing predominantly to the optical emission. We investigate the effects of the resulting surface temperature profiles on the observable lightcurve which an isolated thermally emitting NS would produce for different field geometries. The lightcurves will be both qualitatively (deviations from sinusoidal shape) and quantitatively (larger pulsed fraction for the same observational geometry) different from those of a NS with an isothermal crust. This opens the possibility to determine the internal magnetic field strengths and structures in NSs by modeling their X-ray lightcurves and spectra. The striking similarities of our model calculations with the observed spectra and pulse profiles of isolated thermally emitting NSs is an indication for the existence of strong magnetic field components maintained by crustal currents.

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“…As the magnetic field is divergence-free, its three component can be represented by two scalar potentials, S and T (Chandrasekhar 1961;Rädler 2000):…”

Section: Structure Of the Magnetic Fieldmentioning

confidence: 99%

Temperature distribution in magnetized neutron star crusts

Geppert¹,

Küker

Page

2006

A&A

101

124

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“…Any solution can be considered as a superposition of a solution of the homogeneous equation, which is independent of B, and a solution of the full equation which is linear and homogeneous in B. If there is a non-decaying solution of the homogeneous equation the mean electromotive force E may have a non-decaying part, say E (0) , independent of B (see, e.g., Rädler 1976Rädler , 2000. If ∇ × E (0) = 0 such solutions correspond to small-scale dynamos.…”

Section: Dynamical Aspectsmentioning

confidence: 99%

“…(see also, e.g., Krause and Rädler 1971, 1980or Rädler 2000. Incidentally, determinations of a ij and b ijk have been done within the framework of numerical simulations of magnetoconvection or dynamos without using the second-order correlation approximation.…”

Section: Dynamical Aspectsmentioning

confidence: 99%

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Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force

Rädler

Rheinhardt

2007

Geophysical & Astrophysical Fluid Dynamics

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There are various analytical approaches to the mean electromotive force E = u × b crucial in mean-field electrodynamics, with u and b being velocity and magnetic field fluctuations. In most cases the traditional approach, restricted to the second-order correlation approximation, has been used. Its validity is only guaranteed for a range of conditions, which is narrow in view of many applications, e.g., in astrophysics. With the intention to have a wider range of applicability other approaches have been proposed which make use of the so-called τ -approximation, reducing correlations of third order in u and b to such of second order. After explaining some basic features of the traditional approach a critical analysis of the approaches of that kind is given. It is shown that they lead in some cases to results which are in clear conflict with those of the traditional approach. It is argued that this indicates shortcomings of the τ -approaches and poses serious restrictions to their applicability. These shortcomings do not result from the basic assumption of the τ -approximation. Instead, they seem to originate in some simplifications made in order to derive E without really solving the equations governing u and b. A starting point for a new approach is described which avoids the conflict.

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“…The possibility of a contribution to E from small-scale dynamo action has been intensively discussed in the literature (e.g. Rädler 1976;Rädler 2000;. It has been used to argue against the applicability of mean-field theory (Cattaneo & Hughes 2009).…”

Section: Discussionmentioning

confidence: 99%

Global dynamo models from direct numerical simulations and their mean-field counterparts

Schrinner

2011

A&A

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Context. The test-field method permits us to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo models with their mean-field counterparts. This has been done to date for a simulation of rotating magnetoconvection and a simple benchmark dynamo, which are both (quasi-)stationary. Aims. It is shown that chaotically time-dependent dynamos in a low Rossby number regime can be appropriately described by corresponding mean-field results. We also identify conditions under which mean-field models disagree with direct numerical simulations. Methods. We solve the equations of magnetohydrodynamics (MHD) in a rotating, spherical shell in the Boussinesq approximation. Based on this, we compute mean-field coefficients for several models with the help of the previously developed test-field method. The parameterization of the mean electromotive force by these coefficients is tested against direct numerical simulations. In addition, we use the determined dynamo coefficients in mean-field models and compare the outcome with azimuthally averaged fields from direct numerical simulations. Results. The azimuthally and time-averaged electromotive force in rapidly rotating dynamos is sufficiently well parameterized by the set of determined mean-field coefficients. In comparison to the previously considered (quasi-)stationary dynamo, the chaotic timedependence leads to an improved scale separation and thus to a closer agreement between direct numerical simulations and mean-field results.

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The Generation of Cosmic Magnetic Fields

Cited by 25 publications

References 84 publications

Temperature distribution in magnetized neutron star crusts

Temperature distribution in magnetized neutron star crusts

Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force

Global dynamo models from direct numerical simulations and their mean-field counterparts

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