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Register a new userAdvances in mean-field dynamo theories
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V. V. Pipin
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We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.
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We explore a response of a non-linear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation which is anchored at r=0.9R has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric with respect to the equator perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on the turbulent magnetic Reynolds number R_m. In the range of R_m=10^{4-6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a non-linear alpha-effect and magnetic buoyancy. In the stationary state the large-scale magnetic field demonstrates a phenomenon of active longitudes with cyclic 180 degree flip-flop changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However this effect disappears in the model which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period, and carries important information about the dynamo process.
We focus on the connection between the internal dynamo magnetic field and the stellar wind. If the star has a cyclic dynamo, the modulations of the magnetic field can affect the wind, which in turn can back-react on the boundary conditions of the star, creating a feedback loop. We have developed a 2.5-dimensional numerical set-up to model this essential coupling. We have implemented an alpha-Omega mean-field dynamo in the PLUTO code, and then coupled it to a spherical polytropic wind model via an interface composed of four grid layers with dedicated boundary conditions. We present here a dynamo model close to a young Sun with cyclic magnetic activity. First we show how this model allows to track the influence of the dynamo activity on the corona by displaying the correlation between the activity cycle, the coronal structure and the time evolution of integrated quantities. Then we add the feedback of the wind on the dynamo and discuss the changes observed in the dynamo symmetry and the wind variations. We explain these changes in terms of dynamo modes : in this parameter regime, the feedback loop leads to a coupling between the dynamo families via a preferred growth of the quadrupolar mode. We also study our interface in terms of magnetic helicity, and show that it leads to a small injection in the dynamo. This model confirms the importance of coupling physically internal and external stellar layers, as it has a direct impact on both the dynamo and the wind.
Extreme solar activity fluctuations and the occurrence of solar grand minima and maxima episodes, are well established, observed features of the solar cycle. Nevertheless, such extreme activity fluctuations and the dynamics of the solar cycle during Maunder minima-like episodes remain ill-understood. We explore the origin of such extreme solar activity fluctuations and the role of dual poloidal field sources, namely the Babcock-Leighton mechanism and the mean-field alpha effect in the dynamics of the solar cycle. We mainly concentrate on entry and recovery from grand minima episodes such as the Maunder minimum and the dynamics of the solar cycle. We use a kinematic solar dynamo model with a novel set-up in which stochastic perturbations force two distinct poloidal field alpha effects. We explore different regimes of operation of these poloidal sources with distinct operating thresholds, to identify the importance of each. The perturbations are implemented independently in both hemispheres which allows one to study the level of hemispheric coupling and hemispheric asymmetry in the emergence of sunspots. From the simulations performed we identify a few different ways in which the dynamo can enter a grand minima episode. While fluctuations in any of the $alpha$ effects can trigger intermittency we find that the mean-field alpha effect is crucial for the recovery of the solar cycle from a grand minima episode which a Babcock-Leighton source alone, fails to achieve. Our simulations also demonstrate other cycle dynamics. We conclude that stochastic fluctuations in two interacting poloidal field sources working with distinct operating thresholds is a viable candidate for triggering episodes of extreme solar activity and that the mean-field alpha effect capable of working on weak, sub-equipartition fields is critical to the recovery of the solar cycle following an extended solar minimum.
We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-year cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the observation and the dynamo model show an exceptional role of the axisymmetric $ell_{5}$ mode. Its origin seems to be readily connected with the formation and evolution of sunspots on the solar surface. The results of observations and dynamo models show a good agreement for the low $ell_{1}$ and $ell_{3}$ modes. The results for these modes do not differ significantly for the axisymmetric and nonaxisymmetric models. Our findings support the idea that the sources of the solar dynamo arise as a result of both the distributed dynamo processes in the bulk of the convection zone and the surface magnetic activity.
The interstellar medium of the Milky Way and nearby disk galaxies harbours large-scale coherent magnetic fields of Microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalise our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent multi-phase interstellar medium. By introducing spatially (temporally) modulated mean fields, we extend the previously used test-field method to the spectral realm -- providing the Fourier representation of the convolution kernels. The resulting spectra of the dynamo mean-field coefficients that we obtain broadly match expectations and allow to rigorously constrain the degree of scale separation in the Galactic dynamo. A surprising result is found for the diamagnetic pumping term, which increases in amplitude when going to smaller scales. Our results amount to the most comprehensive description of dynamo mean-field effects in the Galactic context to date. Surveying the relevant parameter space and quenching behaviour, this will ultimately enable the development of assumption-free sub-grid prescriptions for otherwise unresolved global galaxy simulations.
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