In the paper we study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density pattern around the bipolar regions depends on the configuration of the ambient large-scale magnetic field, and in general they show the quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time-latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions show two bands of sign for the density distribution in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to the surface differential rotation. Examining effect of helicity fluxes from the bipolar regions on the large-scale dynamo we find that its effect to the dynamo saturation is negligible.
The paper address the effects of magnetic helicity conservation in a non-linear nonaxisymmetric mean-field solar dynamo model. We study the evolution of the shallow non-axisymmetric magnetic field perturbation with the strength about 10G in the solar convection zone. The dynamo evolves from the pure axisymmetric stage through the short (about 2 years) transient phase when the non-axisymmetric m=1 dynamo mode is dominant to the final stage where the axisymmetry of the dynamo is almost restored. It is found that magnetic helicity is transferred forth and back over the spectral space during the t…
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 $α$-effect and the helicity fluxes can inverse the causa…
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 hemispheri…
We discuss here a purely hydrodynamical mechanism to invert the sign of the kinetic helicity, which plays a key role in determining the direction of propagation of cyclical magnetism in most models of dynamo action by rotating convection. Such propagation provides a prominent, and puzzling constraint on dynamo models. In the Sun, active regions emerge first at mid-latitudes, then appear nearer the equator over the course of a cycle, but most previous global-scale dynamo simulations have exhibited poleward propagation (if they were cyclical at all). Here, we highlight some simulations in which …
We explore effects of random non-axisymmetric perturbations of kinetic helicity (the $α$ effect) and diffusive decay of bipolar magnetic regions on generation and evolution of large-scale non-axisymmetric magnetic fields on the Sun. Using a reduced 2D nonlinear mean-field dynamo model and assuming that bipolar regions emerge due to magnetic buoyancy in situ of the large-scale dynamo action, we show that fluctuations of the $α$ effect can maintain the non-axisymmetric magnetic fields through a solar-type $α^{2}Ω$ dynamo process. It is found that diffusive decay of bipolar active regions is like…
We investigate the role of magnetic helicity in promoting cyclic magnetic activity in a global, 3D, magnetohydrodynamic (MHD) simulation of a convective dynamo. This simulation is characterized by coherent bands of toroidal field that exist within the convection zone, with opposite polarities in the northern and southern hemispheres. Throughout most of the cycle, the magnetic helicity in these bands is negative in the northern hemisphere and positive in the southern hemisphere. However, during the declining phase of each cycle, this hemispheric rule reverses. We attribute this to a global rest…
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\odot}$ rotating with period of 10 days. For the intermediate value of the parameter of the turbulent magnetic Prandl number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $α$effect. The change of dynamo regime occurs because of the non-axisymme…
The main objective of this paper is to introduce the STABLE (Surface flux Transport And Babcock-LEighton) solar dynamo model. STABLE is a 3D Babcock-Leighton/Flux Transport dynamo model in which the source of poloidal field is the explicit emergence, distortion, and dispersal of bipolar magnetic regions (BMRs). Here we describe the STABLE model in more detail than we have previously and we verify it by reproducing a 2D mean-field benchmark. We also present some representative dynamo simulations, focusing on the special case of kinematic magnetic induction and axisymmetric flow fields. Not all …
The observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large-scale polar fields from sunspots fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields are modeled as an effective turbulent diffusion. We present the first kinematic 3D FT/BL model to explicitly incorporate realistic convective flows based on solar observations. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective m…
Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, mos…
We study effects of the cross-helicity in the full-sphere large-scale mean-field dynamo models of the 0.3M star rotating with the period of 10 days. In exploring several dynamo scenarios which are stemming from the cross-helicity generation effect, we found that the cross-helicity provide the natural generation mechanisms for the large-scale scale axisym- metric and non-axisymmetric magnetic field. Therefore the rotating stars with convective envelope can produce the large-scale magnetic field generated solely due to the turbulent cross-helicity effect (we call it γ 2 -dynamo). Using mean-fiel…
Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2…
A milestone of dynamo theory is Cowling's theorem, known in its modern form as the impossibility for an axisymmetric velocity field to generate an axisymmetric magnetic field by dynamo action. Using an anisotropic electrical conductivity we show that an axisymmetric dynamo is in fact possible with a motion as simple as solid body rotation. On top of that the instability analysis can be conducted entirely analytically, leading to an explicit expression of the dynamo threshold which is the only example in dynamo theory.
The relative importance of the helicity and cross-helicity electromotive dynamo effects for self-sustained magnetic field generation by chaotic thermal convection in rotating spherical shells is investigated as a function of shell thickness. Two distinct branches of dynamo solutions are found to coexist in direct numerical simulations for shell aspect ratios between 0.25 and 0.6 - a mean-field dipolar regime and a fluctuating dipolar regime. The properties characterising the coexisting dynamo attractors are compared and contrasted, including differences in temporal behavior and spatial structu…
We study turbulent generation of large-scale magnetic fields using nonlinear dynamo models for solar-type stars in the range of rotational periods from 14 to 30 days. Our models take into account non-linear effects of dynamical quenching of magnetic helicity, and escape of magnetic field from the dynamo region due to magnetic buoyancy. The results show that the observed correlation between the period of rotation and the duration of activity cycles can be explained in the framework of a distributed dynamo model with a dynamical magnetic feedback acting on the turbulent generation either from ma…
A dynamo model is presented, based on a previously introduced kinematic model, in which the reaction of the magnetic field on the mass flow through the Lorentz force is included. Given the base mass flow corresponding to the case with no magnetic field, and assuming that the modification of this flow due to the Lorentz force can be treated as a perturbation, a complete model of the large-scale magnetic field dynamics can be obtained. The input needed consists in the large-scale meridional and zonal flows, the small-scale magnetic diffusivity, and a constant parameter entering the expression of…
We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behavior of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instabil…
Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of t…
We propose a novel approach to reconstruct the surface magnetic helicity density on the Sun or sun-like stars. The magnetic vector potential is determined via decomposition of vector magnetic field measurements into toroidal and poloidal components. The method is verified using data from a non-axisymmetric dynamo model. We apply the method to vector field synoptic maps from Helioseismic and Magnetic Imager (HMI) onboard of Solar Dynamics Observatory (SDO) to study evolution of the magnetic helicity density during solar cycle 24. It is found that the mean helicity density of the non-axisymmetri…
We seek to understand the transition from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation using 3D numerical simulations of turbulent convection and considering rotation rates between 1 and 30 times the solar value. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration co…
The solar cycle appears to be remarkably synchronized with the gravitational torques exerted by the tidally dominant planets Venus, Earth and Jupiter. Recently, a possible synchronization mechanism was proposed that relies on the intrinsic helicity oscillation of the current-driven Tayler instability which can be stoked by tidal-like perturbations with a period of 11.07 years. Inserted into a simple alpha-Omega dynamo model these resonantly excited helicity oscillations led to a 22.14 years dynamo cycle. Here, we assess various alternative mechanisms of synchronization. Specifically we study a…
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property …
A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $α$--$Ω$-type models mainly in two points. First, in addition to the usual $α$ (helicity effect) and $β$ (turbulent magnetic diffusivity), we consider the $γ$ coefficient (c…
We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancelation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional alpha effect-type dynamo-generated magnetic field with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistic…
Employing the standard solar interior model as input we construct a dynamically-consistent nonlinear dynamo model that takes into account the detailed description of the Λ- effect, turbulent pumping, magnetic helicity balance, and magnetic feedback on the differential rotation and meridional circulation. The background mean-field hydrodynamic model of the solar convection zone accounts the solar-like angular velocity profile and the double-cell meridional circulation. We investigate an impact of the nonlinear magnetic field generation effects on the long-term variability and properties of the …
The cross helicity (velocity--magnetic-field correlation) effects in the magnetic-field induction and momentum transport in the magnetohydrodynamic (MHD) turbulence are investigated with the aid of the multiple-scale renormalized perturbation expansion analysis. The outline of the theory is presented with reference to the role of the cross-interaction response functions between the velocity and magnetic field. In this formulation, the expressions of the turbulent fluxes: the turbulent electromotive force (EMF) in the mean induction equation and the Reynolds and turbulent Maxwell stresses in th…
A turbulent dynamo in spherical geometry with an outer corona is simulated to study the sign of magnetic helicity in the outer parts. In agreement with earlier studies, the sign in the outer corona is found to be opposite to that inside the dynamo. Line-of-sight observations of polarized emission are synthesized to explore the feasibility of using the local reduction of Faraday depolarization to infer the sign of helicity of magnetic fields in the solar corona. This approach was previously identified as an observational diagnostic in the context of galactic magnetic fields. Based on our simula…
Obtaining observational constraints on the role of turbulent effects for the solar dynamo is a difficult, yet crucial, task. Without such knowledge, the full picture of the operation mechanism of the solar dynamo cannot be formed. The magnetic helicity spectrum provides important information about the $α$ effect. Here we demonstrate a formalism in spherical geometry to infer magnetic helicity spectra directly from observations of the magnetic field, taking into account the sign change of magnetic helicity across the Sun's equator. Using an angular correlation function of the magnetic field, we…
