Rotational threshold in global numerical dynamo simulations

Magnetic field observations of low-mass stars reveal an increase of magnetic activity with increasing rotation rate. The so-called activity-rotation relation is usually attributed to changes in the underlying dynamo processes generating the magnetic field. We examine the dependence of the field strength on rotation in global numerical dynamo models and interpret our results on the basis of energy considerations. In agreement with the scaling law proposed by Christensen & Aubert (2006), the field strength in our simulations is set by the fraction of the available power used for the magnetic field generation. This is controlled by the dynamo efficiency calculated as the ratio of Ohmic to total dissipation in our models. The dynamo efficiency grows strongly with increasing rotation rate at a Rossby number of 0.1 until it reaches its upper bound of one and becomes independent of rotation. This gain in efficiency is related to the strong rotational dependence of the mean electromotive force in this parameter regime. For multipolar models at Rossby numbers clearly larger than 0.1, on the other hand, we do not find a systematic dependence of the field strength on rotation. Whether the enhancement of the dynamo efficiency found in our dipolar models explains the observed activity-rotation relation needs to be further assessed.Comment: 6 pages, 4 figure

Dipole Collapse and Dynamo Waves in Global Direct Numerical Simulations

Magnetic fields of low-mass stars and planets are thought to originate from self-excited dynamo action in their convective interiors. Observations reveal a variety of field topologies ranging from large-scale, axial dipole to more structured magnetic fields. In this article, we investigate more than 70 three-dimensional, self-consistent dynamo models obtained by direct numerical simulations. The control parameters, the aspect ratio and the mechanical boundary conditions have been varied to build up this sample of models. Both, strongly dipolar and multipolar models have been obtained. We show that these dynamo regimes can in general be distinguished by the ratio of a typical convective length scale to the Rossby radius. Models with a predominantly dipolar magnetic field were obtained, if the convective length scale is at least an order of magnitude larger than the Rossby radius. Moreover, we highlight the role of the strong shear associated with the geostrophic zonal flow for models with stress-free boundary conditions. In this case, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos co-exist. We interpret our results in terms of dynamo eigenmodes using the so-called test-field method. We can thus show that models in the dipolar regime are characterized by an isolated 'single mode'. Competing overtones become significant as the boundary to multipolar dynamos is approached. We discuss how these findings relate to previous models and to observations.Comment: 35 pages, 16 figure

Mode analysis of numerical geodynamo models

It has been suggested in Hoyng (2009) that dynamo action can be analysed by expansion of the magnetic field into dynamo modes and statistical evaluation of the mode coefficients. We here validate this method by analysing a numerical geodynamo model and comparing the numerically derived mean mode coefficients with the theoretical predictions. The model belongs to the class of kinematically stable dynamos with a dominating axisymmetric, antisymmetric with respect to the equator and non-periodic fundamental dynamo mode. The analysis requires a number of steps: the computation of the so-called dynamo coefficients, the derivation of the temporally and azimuthally averaged dynamo eigenmodes and the decomposition of the magnetic field of the numerical geodynamo model into the eigenmodes. For the determination of the theoretical mode excitation levels the turbulent velocity field needs to be projected on the dynamo eigenmodes. We compare the theoretically and numerically derived mean mode coefficients and find reasonably good agreement for most of the modes. Some deviation might be attributable to the approximation involved in the theory. Since the dynamo eigenmodes are not self-adjoint a spectral interpretation of the eigenmodes is not possible

Topology and field strength in spherical, anelastic dynamo simulations

Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings.Comment: 14 pages, 11 figure

Mechanisms of Planetary and Stellar Dynamos

We review some of the recent progress on modeling planetary and stellar dynamos. Particular attention is given to the dynamo mechanisms and the resulting properties of the field. We present direct numerical simulations using a simple Boussinesq model. These simulations are interpreted using the classical mean-field formalism. We investigate the transition from steady dipolar to multipolar dynamo waves solutions varying different control parameters, and discuss the relevance to stellar magnetic fields. We show that owing to the role of the strong zonal flow, this transition is hysteretic. In the presence of stress-free boundary conditions, the bistability extends over a wide range of parameters.Comment: Proceedings of IAUS 294 "Solar and Astrophysical Dynamos and Magnetic Activity" Editors A.G. Kosovichev, E.M. de Gouveia Dal Pino, & Y.Yan, Cambridge University Press, to appear (2013

Die Besteuerung von Alterseinkünften und des Altersvorsorgesparens

Die Krise der gesetzlichen Rentenversicherung lenkt das öffentliche Interesse auf andere Instrumente der Altersvorsorge. Können betriebliche und private Altersvorsorge die sich auftuende Lücke schließen? Voraussetzung für eine effiziente Altersvorsorge ist eine neutrale Besteuerung aller Vorsorgewege

Die Besteuerung von Alterseinkünften und des Altersvorsorgesparens

Die Krise der gesetzlichen Rentenversicherung lenkt das öffentliche Interesse auf andere Instrumente der Altersvorsorge. Können betriebliche und private Altersvorsorge die sich auftuende Lücke schließen? Voraussetzung für eine effiziente Altersvorsorge ist eine neutrale Besteuerung aller Vorsorgewege. --

Mean-field effects in the Galloway-Proctor flow

The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general nonzero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity eta_t and a related quantity are given, too. Finally a result for alpha in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the alpha effect and related effects in flows that are statistical isotropic in a plane.Comment: 12 pages, 14 figures, submitted to MNRA

Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers

We discuss the applicability of the kinematic $\alpha$-effect formalism at high magnetic Reynolds numbers. In this regime the underlying flow is likely to be a small-scale dynamo, leading to the exponential growth of fluctuations. Difficulties arise with both the actual calculation of the $\alpha$ coefficients and with its interpretation. We argue that although the former may be circumvented -- and we outline several procedures by which the the $\alpha$ coefficients can be computed in principle -- the interpretation of these quantities in terms of the evolution of the large-scale field may be fundamentally flawed.Comment: 5 pages, LaTeX, no figure