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Register a new userA Solar Dynamo Model Driven by Mean-Field Alpha and Babcock-Leighton Sources: Fluctuations, Grand-Minima-Maxima and Hemispheric Asymmetry in Sunspot Cycles
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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.
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The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. In this work, we have explored the effects of the turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. The results reveal the importance of the pumping mechanism for solving current limitations in mean field dynamo modeling such as the storage of the magnetic flux and the latitudinal distribution of the sunspots. In the case that a meridional flow is assumed to be present only in the upper part of the convective zone, it is the full turbulent pumping that regulates both the period of the solar cycle and the latitudinal distribution of the sunspots activity.
We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha-coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over a suitable parameter range. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model, or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.
We aim to investigate the nature and occurrence characteristics of grand solar minimum and maximum periods, which are observed in the solar proxy records such as 10Be and 14C, using a fully non-linear Babcock-Leighton type flux-transport dynamo including momentum and entropy equations. The differential rotation and meridional circulation are generated from the effect of turbulent Reynolds stress and are subjected to back-reaction from the magnetic field. To generate grand minimum and maximum-like periods in our simulations, we used random fluctuations in the angular momentum transport process, namely the Lambda-mechanism, and in the Babcock-Leighton mechanism. To characterise the nature and occurrences of the identified grand minima and maxima in our simulations, we used the waiting time distribution analyses, which reflects whether the underlying distribution arises from a random or a memory-bearing process. The results show that, in majority of the cases, the distributions of grand minima and maxima reveal that the nature of these events originates from memoryless processes. We also found that in our simulations the meridional circulation speed tends to be smaller during grand maximum, while it is faster during grand minimum periods. The radial differential rotation tend to be larger during grand maxima, while it is smaller during grand minima. The latitudinal differential rotation on the other hand is found to be larger during grand minima.
Context. Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. Solutions with high-magnetic-diffusivity have too short periods and a wrong migration of their active belts. Only the low-diffusivity regime with advective meridional flows is usually considered. Aims. In the present paper we discuss these assumptions and applied a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes which supposedly form at the tachocline. We study the effect of the delay, which adds to the spacial non-locality a non-linear temporal one, in the advective but particularly in the diffusive regime. Methods. Fournier et al. (2017) obtained the rise time according to stellar parameters such as rotation, and the magnetic field strength at the bottom of the convection zone. These results allowed us to constrain the delay in the mean-field model used in a parameter study. Results. We identify an unknown family of solutions. These solutions self-quench, and exhibit longer periods than their non-delayed counterparts. Additionally, we demonstrate that the non-linear delay is responsible for the recover of the equatorward migration of the active belts at high turbulent diffusivities. Conclusions. By introducing a non-linear temporal non-locality (the delay) in a Babcock-Leighton dynamo model, we could obtain solutions quantitatively comparable to the solar butterfly diagram in the diffusion-dominated regime.
In this paper we study the effects of hemispheric imbalance of magnetic helicity density on breaking the equatorial reflection symmetry of the dynamo generated large-scale magnetic field. Our study employs the axisymmetric dynamo model which takes into account the nonlinear effect of magnetic helicity conservation. We find that the evolution of the net magnetic helicity density, in other words, the magnetic helicity imbalance, on the surface follows the evolution of the parity of the large-scale magnetic field. Random fluctuations of the $alpha$-effect and the helicity fluxes can inverse the causal relationship, i.e., the magnetic helicity imbalance or the imbalance of magnetic helicity fluxes can drive the magnetic parity breaking. We also found that evolution of the net magnetic helicity of the small-scale fields follows the evolution of the net magnetic helicity of the large-scale fields with some time lag. We interpret this as an effect of the difference of the magnetic helicity fluxes out of the Sun from the large and small scales.
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