We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about ?/2, which can be explained by an oscillatory ?2 dynamo caused by the sign change of the ?-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2? azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.

Effects of enhanced stratification on equatorward dynamo wave propagation

Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, ηt, is proportional to the square of the turbulent vertical velocity in all cases. Whereas ηt decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω × J-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

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Alpha effect and turbulent diffusion from convection

Context. Solar magnetic activity shows both smooth secular changes, such as the modern Grand Maximum, and quite abrupt drops that are denoted as grand minima, such as the Maunder Minimum. Direct numerical simulations (DNS) of convection-driven dynamos offer one way of examining the mechanisms behind these events.Aims. In this work, we analyze a solution of a solar-like DNS that was evolved for roughly 80 magnetic cycles of 4.9 years and where epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. Methods. The DNS employed is a semi-global (wedge-shaped) magnetoconvection model. For the data analysis tasks we use Ensemble Empirical Mode Decomposition and phase dispersion methods, as they are well suited for analyzing cyclic (non-periodic) signals.Results. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like (equatorward migration at low latitudes and poleward at high latitudes). This mode is accompanied by a higher frequency mode near the surface and at low latitudes, showing poleward migration, and a low-frequency mode at the bottom of the convection zone. The low-frequency mode is almost purely antisymmetric with respect to the equator, while the dominant mode has strongly fluctuating mixed parity. The overall behavior of the dynamo solution is extremely complex, exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum; during this epoch the bottom toroidal magnetic field obtains a maximum, demonstrating that the interpretation of grand minima-type events is non-trivial. The hemispherical asymmetries are seen only in the magnetic field, while the velocity field exhibits considerably weaker asymmetry. Conclusions. We interpret the overall irregular behavior as being due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low-activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses.

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Multiple dynamo modes as a mechanism for long-term solar activity variations

Prediction of the Sun's magnetic activity is important because of its effect on space environment and climate. However, recent efforts to predict the amplitude of the solar cycle have resulted in diverging forecasts with no consensus. Yeates et al. have shown that the dynamical memory of the solar dynamo mechanism governs predictability, and this memory is different for advection- and diffusion-dominated solar convection zones. By utilizing stochastically forced, kinematic dynamo simulations, we demonstrate that the inclusion of downward turbulent pumping of magnetic flux reduces the memory of both advection- and diffusion-dominated solar dynamos to only one cycle; stronger pumping degrades this memory further. Thus, our results reconcile the diverging dynamo-model-based forecasts for the amplitude of solar cycle 24. We conclude that reliable predictions for the maximum of solar activity can be made only at the preceding minimum-allowing about five years of advance planning for space weather. For more accurate predictions, sequential data assimilation would be necessary in forecasting models to account for the Sun's short memory.

http://iopscience.iop.org/article/10.1088/2041-8205/761/1/L13/pdf

Turbulent Pumping of Magnetic Flux Reduces Solar Cycle Memory and thus Impacts Predictability of the Sun's Activity

We propose a solar dynamo model distributed in the bulk of the convection zone with toroidal magnetic-field flux concentrated in a near-surface layer. We show that if the boundary conditions at the top of the dynamo region allow the large-scale toroidal magnetic fields to penetrate close to the surface, then the modeled butterfly diagram for the toroidal magnetic field in the upper convection zone is formed by the subsurface rotational shear layer. The model is in agreement with observed properties of the magnetic solar cycle.

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THE SUBSURFACE-SHEAR-SHAPED SOLAR αΩ DYNAMO

Context. The standard dynamo model for the solar and stellar magnetic fields is based on the αΩ mechanism, namely, an interplay between differential rotation (the Ω effect) and a mean electromotive force generated by helical turbulent convection flows (the α effect). There are, however, a number of problems with the α effect and αΩ dynamo models. Two of them are that, in the case of the Sun, the obtained cycle periods are too short and the magnetic activity is not sufficiently concentrated at low latitudes. Aims. We explore the role of turbulent induction effects that may appear in addition to the α effect. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the Ω × J effect. We also include anisotropic diffusion and a new dynamo term that is of third order in the rotation vector Ω. Methods. We studied axisymmetric mean-field dynamo models containing differential rotation, the α effect, and the additional turbulent induction effects. The model calculations were carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. In addition, we consider a dynamo model for a full sphere that is based solely on the joint induction effects of rotation and an inhomogeneity of the large-scale magnetic field, without differential rotation and the α effect (a δ 2 dynamo model). This kind of dynamo model may be relevant for fully convective stars. Results. With respect to the solar dynamo, the inclusion of the additional turbulent induction effects increases the period of the dynamo and brings the large-scale toroidal field closer to the equator, thus improving the agreement of the models with the observations. For the δ 2 dynamo working in a full sphere, we find dynamo modes that are steady if the effect of anisotropic diffusion is not included. The inclusion of anisotropic diffusion yields a magnetic field oscillating with a period close to the turbulent magnetic diffusion time.

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Stellar dynamos with Ω × J effect

We present a straightforward comparison of model calculations for the α-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the α-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 – 15∘. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model.

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The Alpha Effect and the Observed Twist and Current Helicity of Solar Magnetic Fields

Context. Most solar and stellar dynamo models use the $\alpha\Omega$ scenario where the magnetic field is generated by the interplay between differential rotation (the Ω effect) and a mean electromotive force due to helical turbulent convection flows (the α effect). There are, however, turbulent dynamo mechnisms that may complement the α effect or may be an alternative to it. Aims. We investigate models of solar-type dynamos where the α effect is completely replaced by two other turbulent dynamo mechanisms, namely the $\vec{\Omega}\times \vec{J}$ effect and the shear-current effect, which both result from an inhomogeneity of the mean magnetic field. Methods. We studied axisymmetric mean-field dynamo models containing differential rotation, the $\vec{\Omega}\times\vec{J}$ and shear-current effects, and a meridional circulation. The model calculations were carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. Results. Without meridional flow, no satisfactory agreement of the models with the solar observations can be obtained. With a sufficiently strong meridional circulation included, however, the main properties of the large-scale solar magnetic field, namely, its oscillatory behavior, its latitudinal drift towards the equator within each half cycle, and its dipolar parity with respect to the equatorial plane, are correctly reproduced. Conclusions. We have thereby constructed the first mean-field models of solar-type dynamos that do not use the α effect.

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Valerij V. Pipin

Papers

Stellar dynamos with Ω × J effect

The Alpha Effect and the Observed Twist and Current Helicity of Solar Magnetic Fields

An advective solar-type dynamo without the α effect