Complete Alpha-Tensor for Solar Dynamo

Krivodubskij, V. N.; Schultz, M.

doi:10.1007/978-94-011-0772-3_4

Cited by 7 publications

(10 citation statements)

References 1 publication

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“…While being an important ingredient in theories of an αΩ dynamo in the solar overshoot layer (e.g. Rüdiger & Brandenburg 1995), the α effect due to the stratification of the turbulence is of minor importance in the bulk of the solar convection zone, or in a fully convective star (Krivodubskij & Schultz 1993). The contribution of the density stratification reads (Kitchatinov & Rüdiger 1992;Rüdiger & Hollerbach 2004):…”

Section: The α Effectmentioning

confidence: 99%

Large-scale $\vec \alpha\mathsf{^2}$-dynamo in low-mass stars and brown dwarfs

Chabrier¹,

Kueker²

2006

A&A

211

218

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We develop a model based on three dimensional mean-field magnetohydrodynamics computations for the generation of large scale magnetic fields in fully convective objects like low-mass stars, brown dwarfs and possibly gaseous planets. The dynamo process is of α 2 type and thus differs from the shell-dynamo at work in more massive stars. The α 2 dynamo is found to become supercritical for Coriolis numbers Ω > ∼ 1, i.e. Rossby numbers Ro < ∼ 10. It generates a large-scale, non-axisymmetric, steady field that is symmetric with respect to the equatorial plane. Saturation of the α 2 -generated field at the equipartition field strength yields strengths of several kiloGauss, in agreement with observations of active M dwarfs, and provides a qualitative explanation for the observed activity saturation in late M stars. For brown dwarfs with a conductive core, as occurs at the center of the most massive and oldest of these objects, we have also studied an α 2 Ω dynamo, i.e. the effect of differential rotation. In this case the field is predominantly toroidal, axisymmetric, and oscillatory, like the solar magnetic field. The topology of the field in the fully convective objects exhibits a high order multipole character that differs from the aligned dipole field generated by the αΩ dynamo. The strong reduction of the dipolar component due to the non-axisymmetry of the field should considerably reduce the Alfven radius and thus the efficiency of magnetic braking, providing an appealing explanation for the decreasing angular momentum loss rate observed in low-mass stars and brown dwarfs. This may have also implications for cataclysmic variables below the period gap. In spite of this large-scale field, the decreasing conductivity in the dominantly neutral atmosphere of these objects may prevent the current generation necessary to support a chromosphere and thus activity. An observational signature of the present model would be (i) asymmetry of the chromospheric activity, contrary to the spatially uniform activity expected from small-scale turbulent dynamo and (ii) the absence of cycles in uniformly rotating (fully convective) low-mass objects.

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Section: The α Effectmentioning

confidence: 99%

Large-scale $\vec \alpha\mathsf{^2}$-dynamo in low-mass stars and brown dwarfs

Chabrier¹,

Kueker²

2006

A&A

211

218

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“…Note that solutions analogous to (57) and (58) were obtained in papers [11,22,28,41]. The dependence of the distribution N(η) on η = p/p 0 is illustrated in figure 7, where the parameter λ, defined by the diffusion coefficient (52), is unity, and the values τ e (8) are denoted near the curves. The absolute value of the spectrum index increases, providing the momentum increases.…”

Section: Particle Acceleration In a Homogeneous Spacementioning

confidence: 68%

Statistical acceleration of energetic particles and their diffusion in turbulent magnetic fields

Fedorov

Shakhov

Stehlík

2012

J. Phys. B: At. Mol. Opt. Phys.

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Two processes of statistical cosmic ray (CR) acceleration and CR diffusion in turbulent magnetic fields are studied. It is assumed that the charged particles gain energy in a bounded space region and then they leave the acceleration region as a result of the spatial diffusion caused by particle scattering in the turbulent inhomogeneous medium. Both the second-order Fermi acceleration and the acceleration by the induced electric field (α-mechanism) are considered. Analytical solutions of the CR transport equation by the Fourier–Laplace method are obtained for various spatial diffusion coefficients. The equilibrium energetic spectra and the spatial distributions of CRs inside and outside the acceleration region are investigated.

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“…Note the different contributions by density gradient and turbulence intensity distribution. The α-effect becomes negative only at the bottom of the convection zone (Krivodubskij and Schultz, 1993). …”

Section: A Boundary-layer Dynamo For the Sunmentioning

confidence: 98%

“…In our computation with molecular diffusion coefficient values the toroidal field amplitude never did exceed 1 kGauss, independent of the radial magnetic field applied. Krivodubskij and Schultz (1993) (with the inclusion of the depth-dependence of the Coriolis number Ω * and using a mixing-length model) derived a profile of the α-effect ( Fig. 7) with a magnitude of 100 m/s, positive in the convection zone and negative in the overshoot layer.…”

Section: A Boundary-layer Dynamo For the Sunmentioning

confidence: 99%

Physics of the solar cycle

Rüdiger¹,

Arlt²

2003

Advances in Nonlinear Dynamos

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The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force as well as the theory of differential rotation and meridional circulation is described for use in dynamo theory. Activity cycles of dynamos in the overshoot layer (BL-dynamo) and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo is able to reproduce the solar cycle periods and the butterfly diagram only if α = 0 in the convection zone. The problems of too many magnetic belts and too short cycle times emerge if the overshoot layer is too thin. The distributed dynamo including meridional flows with a magnetic Reynolds number Rm > ∼ 20 (low magnetic Prandtl number) reproduces the observed butterfly diagram even with a positive dynamo-α in the bulk of the convection zone. The nonlinear feedback of strong magnetic fields on differential rotation in the mean-field conservation law of angular momentum leads to grand minima in the cyclic activity similar to those observed. The 2D model described here contains the large-scale interactions as well as the small-scale feedback of magnetic fields on differential rotation and induction in terms of a mean-field formulation (Λ-quenching, α-quenching). Grand minima may also occur if a dynamo occasionally falls below its critical eigenvalue. We expressed this idea by an on-off α function which is non-zero only in a certain range of magnetic fields near the equipartition value. We never found any indication that the dynamo collapses by this effect after it had once been excited. The full quenching of turbulence by strong magnetic fields in terms of reduced induction (α) and reduced turbulent diffusivity (η T ) is studied with a 1D model. The full quenching results in a stronger dependence of cycle period on dynamo number compared with the model with α-quenching alone giving a very weak cycle period dependence. Also the temporal fluctuations of α and η T from a random-vortex simulation were applied to a dynamo model. Then the low 'quality' of the solar cycle can be explained with a relatively small number of giant cells acting as the dynamo-active turbulence. The simulation contains the transition from almost regular magnetic oscillations (many vortices) to a more or less chaotic time series (very few vortices).

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Complete Alpha-Tensor for Solar Dynamo

Cited by 7 publications

References 1 publication

Large-scale $\vec \alpha\mathsf{^2}$-dynamo in low-mass stars and brown dwarfs

Large-scale $\vec \alpha\mathsf{^2}$-dynamo in low-mass stars and brown dwarfs

Statistical acceleration of energetic particles and their diffusion in turbulent magnetic fields

Physics of the solar cycle

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