The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric-average of the dynamically quenched diffusivity. Here, we provide an analytic fit to the dynamically quenched diffusivity profile, which can be used in kinematic dynamo simulations. Having successfully reconciled the mixing-length theory estimated diffusivity profile with kinematic dynamo models, we argue that they remain a viable tool for understanding the solar magnetic cycle.
The magnetic fields of solar-type stars are observed to cycle over decadal periods -11 years in the case of the Sun. The fields originate in the turbulent convective layers of stars and have a complex dependency upon stellar rotation rate. We have performed a set of turbulent global simulations that exhibit magnetic cycles varying systematically with stellar rotation and luminosity. We find that the magnetic cycle period is inversely proportional to the Rossby number, which quantifies the influence of rotation on turbulent convection. The trend relies on a fundamentally non-linear dynamo proce…
We investigated the dependence of the solar magnetic parity between the hemispheres on two important parameters, the turbulent diffusivity and the meridional flow, by means of axisymmetric kinematic dynamo simulations based on the flux-transport dynamo model. It is known that the coupling of the magnetic field between hemispheres due to turbulent diffusivity is an important factor for the solar parity issue, but the detailed criterion for the generation of the dipole field has not been investigated. Our conclusions are as follows. (1) The stronger diffusivity near the surface is more likely to…
We study the influence of various magnetic diffusivity profiles on the evolution of the poloidal and toroidal magnetic fields in a kinematic flux transport dynamo model for the Sun. The diffusivity is a poorly understood ingredient in solar dynamo models. We mathematically construct various theoretical profiles of the depth-dependent diffusivity, based on constraints from mixing length theory and turbulence, and on comparisons of poloidal field evolution on the Sun with that from the flux-transport dynamo model. We then study the effect of each diffusivity profile in the cyclic evolution of th…
Using direct numerical simulations, we verify that "flow IV" of Roberts (1972) exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above $\approx8$. As expected for a dynamo of this type, but contrary to $α$-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase …
In the non-linear phase of a dynamo process, the back-reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification (the alpha-quenching effect) and the turbulent magnetic diffusivity (the eta-quenching effect). While the former has been widely explored, the effects of eta-quenching in the magnetic field evolution have rarely been considered. In this work we investigate the role of the suppression of diffusivity in a flux-transport solar dynamo model that also includes a non-linear …
In this paper we address a discrepancy between the surface flux evolution in a 3D kinematic dynamo model and a 2D surface flux transport model that has been closely calibrated to the real Sun. We demonstrate that the difference is due to the connectivity of active regions to the toroidal field at the base of the convection zone, which is not accounted for in the surface-only model. Initially, we consider the decay of a single active region, firstly in a simplified Cartesian 2D model and subsequently the full 3D model. By varying the turbulent diffusivity profile in the convection zone, we find…
Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock-Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in butterfly diagram, whereas the presence of a …
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…
Guided by the recent observational result that the meridional circulation of the Sun becomes weaker at the time of the sunspot maximum, we have included a parametric quenching of the meridional circulation in solar dynamo models such that the meridional circulation becomes weaker when the magnetic field at the base of the convection zone is stronger. We find that a flux transport solar dynamo tends to become unstable on including this quenching of meridional circulation if the diffusivity in the convection zone is less than about 2 * 10^{11} cm^2/s. The quenching of alpha, however, has a stabi…
The alpha effect is known to be an indispensable energy source of the poloidal magnetic field in the sun or planet. However, the alpha effect is quenched as the magnetic field grows due to the conservation of magnetic helicity. With these conventional understanding, what indeed generates and sustains the observed poloidal magnetic field remains a mystery. To solve this contradiction between theory and real nature, we derived a semi-analytic representation of alpha and beta using large scale magnetic helicity and energy. Applying the simulation data to alpha and beta, we found that the negative…
The surface flux transport (SFT) model of solar magnetic fields involves empirically well-constrained velocity and magnetic fields. The basic evolution of the Sun's large-scale surface magnetic field is well described by this model. The azimuthally averaged evolution of the SFT model can be compared to the surface evolution of the flux transport dynamo (FTD), and the evolution of the SFT model can be used to constrain several near-surface properties of the FTD model. We compared the results of the FTD model with different upper boundary conditions and diffusivity profiles against the results o…
The meridional circulation plays an essential role in determining the basic mechanism of the dynamo action in case the of a low eddy diffusivity. Flux-transport dynamos with strong return flow and a deep stagnation point are discussed in the case of a positive $α$-effect located in the overshoot layer and a rotation law consistent with helioseismology. By means of a linear dynamo model, it will be shown that the migration of the toroidal belts at lower latitudes and the periods of the activity cycles are consistent with the observations. Moreover, at variance with previous investigations, the …
In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev. Lett. 109, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behavior is different from that of an alpha^2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For th…
The existence of a tachocline in the Sun has been proven by helioseismology. It is unknown whether a similar shear layer, widely regarded as the seat of magnetic dynamo action, also exists in a protoneutron star. Sudden jumps in magnetic diffusivity $η$ and turbulent vorticity $α$, for example at the interface between the neutron-finger and convective zones, are known to be capable of enhancing mean-field dynamo effects in a protoneutron star. Here we apply the well-known, plane-parallel, MacGregor-Charbonneau analysis of the Solar interfacial dynamo to the protoneutron star problem and calcul…
We derive the advection of magnetic fields due to gradients in magnetic diffusivity, starting from the magnetic induction equation. We discuss physical examples, and compare our results to those in the literature. Our induction and diffusion equations may be useful in solar dynamo studies, and for space and laboratory plasmas.
We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the multiscale stability theory. It turns out that, due to the magnetic $α$-effect in such flows, the large-scale mean field experiences harmonic oscillations in time on the scale O($\varepsilon t$) without growth or decay. Here $\varepsilon$ is the spatial scale ratio and $t$ is the fast time of the order of the flow turnover time. The interaction of the accompanying fluctuating magnetic field with the flow gives rise to an…
A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit-type. The flows are unstable against nonaxisymmetric perturbations which form electromotive forces defining $α$ effect and eddy diffusivity. If both degenerated modes with $m=\pm 1$ are excited with the same power then the global $α$ effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite $α$ effects if only an isolated mode is considered but this intrinsic helicity of the single-mode…
Magnetohydrodynamic interactions between plasma flows and magnetic fields is fundamental to the origin and sustenance of the 11-year sunspot cycle. These processes are intrinsically three-dimensional (3D) in nature. Our goal is to construct a 3D solar dynamo model that on the one hand captures the buoyant emergence of tilted bipolar sunspot pairs, and on the other hand produces cyclic large-scale field reversals mediated via surface flux-transport processes -- that is, the Babcock-Leighton mechanism. We perform kinematic dynamo simulations where the prescribed velocity field is a combination o…
We point out the difficulties in carrying out direct numerical simulation of the solar dynamo problem and argue that kinematic mean-field models are our best theoretical tools at present for explaining various aspects of the solar cycle in detail. The most promising kinematic mean-field model is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock--Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. Depending on whether the diffusivity is high o…
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 del…
We analyze the nature of dynamo action that produces horizontally averaged magnetic fields in two particular flows that were studied by Roberts (1972, Phil. Trans. R. Soc. A 271, 411), namely his flows II and III. They have zero kinetic helicity either pointwise (flow II), or on average (flow III). Using direct numerical simulations, we determine the onset conditions for dynamo action at moderate values of the magnetic Reynolds number. Using the test-field method, we show that the turbulent magnetic diffusivity is then positive for both flows. However, we demonstrate that for both flows large-…
Solar magnetic fields comprise an 11-year activity cycle, represented by the number of sunspots. The maintenance of such a solar magnetic field can be attributed to fluid motion in the convection zone, i.e. a dynamo. This study conducts the mean-field analyses of the global solar dynamo simulation presented by Hotta et al. (2016). Although the study succeeds in producing coherent large-scale magnetic fields at high Reynolds numbers, the detailed physics of the maintenance of this field have not been fully understood. This study extracts the alpha-tensor and the turbulent magnetic diffusivity t…
The solar activity cycle is successfully modeled by the flux transport dynamo, in which the meridional circulation of the Sun plays an important role. Most of the kinematic dynamo simulations assume a one-cell structure of the meridional circulation within the convection zone, with the equatorward return flow at its bottom. In view of the recent claims that the return flow occurs at a much shallower depth, we explore whether a meridional circulation with such a shallow return flow can still retain the attractive features of the flux transport dynamo (such as a proper butterfly diagram, the pro…
The transition to intermittent mean--field dynamos is studied using numerical simulations of isotropic magnetohydrodynamic turbulence driven by a helical flow. The low-Prandtl number regime is investigated by keeping the kinematic viscosity fixed while the magnetic diffusivity is varied. Just below the critical parameter value for the onset of dynamo action, a transient mean--field with low magnetic energy is observed. After the transition to a sustained dynamo, the system is shown to evolve through different types of intermittency until a large--scale coherent field with small--scale turbulen…
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 is modeled as an effective turbulent diffusion. Recent SFT models have incorporated explicit, realistic convective flows in order to improve the fidelity of convective transport but, to our knowledge, this has not yet been implemented in previous BL models. Since most Flux-Transport (FT)/BL mode…
We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero mean magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. The calculations begin from an isothermal state spanning three scale heights above and below the mid-plane. After a long transient the layers settle to a stationary state in which thermal losses out of the boundaries are balanced by dissipative heating. We identify two regimes. A conductive regime in which the heat is transported mostly by conduction and the density decreases wit…
Turbulence and chaos play a fundamental role in stellar convective zones through the transportof particles, energy and momentum, and in fast dynamos, through the stretching, twisting and folding of magnetic flux tubes. A particularly revealing way to describe turbulent motions is through the analysis of Lagrangian coherent structures (LCS), which are material lines or surfaces that act as transport barriers in the fluid. We report the detection of Lagrangian coherent structures in helical MHD dynamo simulations with scale separation. In an ABC--flow, two dynamo regimes, a propagating coherent …
A combination of diamagnetic pumping and a nonlocal alpha-effect of the Babcock-Leighton type in a solar dynamo model helps to reproduce observations of solar magnetic activity. The period of the solar cycle can be reproduced without reducing magnetic diffusivity in the bulk of the convection zone below the standard mixing-length value of $10^{13}$ cm$^2$s$^{-1}$. The simulated global fields are antisymmetric about the equator and the toroidal-to-poloidal field ratio is about a thousand. The time-latitude diagrams of magnetic fields in the model without meridional flow, however, differ from ob…
(abidged) Context: Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and 5, respectively). Results: We find that the rotation profiles for high thermal diffusivity show a monotonically increasing angular veloc…
The emergence of tilted bipolar active regions and the dispersal of their flux, mediated via processes such as diffusion, differential rotation and meridional circulation is believed to be responsible for the reversal of the Sun's polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed $α$-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surf…
In this work we use a low order dynamo model and study under which conditions can it reproduce solar grand minima. We begin by building the phase space of a proxy for the toroidal component of the solar magnetic field and we develop a model, derived from mean field dynamo theory, that gives the time evolution of the toroidal field. This model is characterized by a non-linear oscillator whose coefficients retain most of the physics behind dynamo theory. In the derivation of the model we also include stochastic oscillations in the $α$ effect. We found no evidences that stochastic fluctuations in…
In 1969 Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock(1961). Here we present a modification and extension of Leighton's model. Using the axisymmetric component of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the effects of turbulent diffusion at the surface and in the convection …
The sunspot number varies roughly periodically with time. However the individual cycle durations and the amplitudes are found to vary in an irregular manner. It is observed that the stronger cycles are having shorter rise times and vice versa. This leads to an important effect know as the Waldmeier effect. Another important feature of the solar cycle irregularity are the grand minima during which the activity level is strongly reduced. We explore whether these solar cycle irregularities can be studied with the help of the flux transport dynamo model of the solar cycle. We show that with a suit…
We have studied the large scale dynamo process forced with helical magnetic energy. The magnetically driven dynamo is not so well studied as kinetically forced dynamo. It has been thought to represent the amplification of magnetic field in the stellar corona, accretion disk, or plasma lab. However, the interaction between the helical magnetic field and plasma is a more fundamental phenomenon that can be extended to the early Universe. The scale-invariant helical magnetic field not only explains the currently observed large scale astrophysical magnetic fields but also has information on the hor…
Recent findings of helioseismology as well as advances in direct numerical simulations of global dynamics of the Sun have indicated that in each solar hemisphere the meridional circulation forms the two cells along the in the convection zone. We investigate properties of a mean-field solar dynamo with such double-cell meridional circulation. The dynamo model also includes the realistic profile of solar differential rotation (including the tachocline and subsurface shear layer), and takes into account effects of turbulent pumping, anisotropic turbulent diffusivity, and conservation of magnetic …
A model for the solar dynamo, consistent in global flow and numerical method employed with the differential rotation model, is developed. The magnetic turbulent diffusivity is expressed in terms of the entropy gradient, which is controlled by the model equations. The magnetic Prandtl number and latitudinal profile of the alpha-effect are specified by fitting the computed period of the activity cycle and the equatorial symmetry of magnetic fields to observations. Then, the instants of polar field reversals and time-latitude diagrams of the fields also come into agreement with observations. The …
We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the Solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find that the flux rope dynamo is more than an order of magnitude more efficient at converting mechanical energ…
We study how anisotropy of turbulent convection affects diffusion of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magneto-hydrodynamics framework using the minimal $τ$-approximation. We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model, and a distributed-dynamo model with the subsurface rotational shear layer. For both models we investigate effects of the double-cell meridional circulation, recently suggested by helioseismology. We introduce a parameter of anisotropy as a ratio o…
We investigate small-scale dynamo action in the solar convection zone through a series of high resolution MHD simulations in a local Cartesian domain with 1$R_\odot$ (solar radius) of horizontal extent and a radial extent from 0.715 to 0.96$R_\odot$. The dependence of the solution on resolution and diffusivity is studied. For a grid spacing of less than 350 km, the root mean square magnetic field strength near the base of the convection zone reaches 95% of the equipartition field strength (i.e. magnetic and kinetic energy are comparable). For these solutions the Lorentz force feedback on the c…
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…
The mean-field theory of magnetized stellar convection gives rise to the two possibility of distinct instabilities: the large-scale dynamo instability, operating in the bulk of the convection zone, and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation, but the growth rate of NEMPI is suppressed with increasing rotation rates, although recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. We examine quantitatively whether…
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 …
We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is opposite to that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action…
The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean-field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar-type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increase…
Context. Two candidate mechanisms have recently been considered for the nonlinear modulation of solar cycle amplitudes. Tilt quenching (TQ) is a negative feedback between cycle amplitude and the mean tilt angle of bipolar active regions relative to the azimuthal direction; latitude quenching (LQ) consists in a positive correlation between cycle amplitude and average emergence latitude of active regions. Aims. Here we explore the relative importance of and the determining factors behind the LQ and TQ effects. Methods. The degree of nonlinearity induced by TQ, LQ and their combination is systema…
In order to match observed properties of the solar cycle, flux-transport dynamo models require the toroidal magnetic flux to be stored in a region of low magnetic diffusivity, typically located at or below the bottom of the convection zone. We infer the turbulent magnetic diffusivity affecting the toroidal field on the basis of empirical data. We consider the time evolution of mean latitude and width of the activity belts of solar cycles 12--23 and their dependence on cycle strength. We interpret the decline phase of the cycles as a diffusion process. The activity level of a given cycle begins…
The surprising thinness of the solar tachocline is still not understood with certainty today. Among the numerous possible scenarios suggested to explain its radial confinement, one hypothesis is based on Maxwell stresses that are exerted by the cyclic dynamo magnetic field of the Sun penetrating over a skin depth below the turbulent convection zone. Our goal is to assess under which conditions (turbulence level in the tachocline, strength of the dynamo-generated field, spreading mechanism) this scenario can be realized in the solar tachocline. We develop a simplified 1D model of the upper tach…
The paper presents a study of kinematic axisymmetric mean-field dynamo models for a case of the meridional circulation with a deep-seated stagnation point and a strong return flow at the bottom of the convection zone. This kind of circulation follows from mean-field models of the angular momentum balance in the solar convection zone. We show that it is possible for this types of meridional circulation to construct kinematic dynamo models that resemble in some aspects the sunspot magnetic activity cycle. The dynamo model includes turbulent sources of the large-scale poloidal magnetic field prod…
Investigation of the eigenvalue spectra of dynamo solutions, has been proved fundamental for the knowledge of dynamo physics. Earlier, curvature-folding relation on dynamos in Riemannian spaces has been investigated [PPL 2008]. Here, analytical solutions representing general turbulent dynamo filaments are obtained in resistive plasmas. Turbulent diffusivity with vanishing kinetic helicity yields a fast mode for a steady dynamo eigenvalue. The magnetic field lays down on a local frame 2 plane along the filaments embedded in a 3D plasma. Curvature effects plays the role of folding in fast magnet…
The eigenvalues and eigenfunctions of a linear α^{2}-dynamo have been computed for different spatial distributions of an isotropic α-effect. Oscillatory solutions are obtained when αexhibits a sign change in the radial direction. The time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue as an oscillatory eigenfunction with conjugate complex eigenvalues. The close proximity of oscillatory and non-oscillatory solutions may serve as the basic ingredient for reversal models that describe abrupt polarity switches of a dipole induced by noise. W…
Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumbe…
An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy…
Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible, non-helical, homogeneous and isotropic flow. In the Kazantsev dynamo model the statistics of the driving flow are assumed to be instantaneously correlated in time. Here we compare the results of the model with the dynamo properties of a simulated flow that has equivalent spatial characteristics as the Kazantsev flow but different temporal statistics. In particular, …
The sunspot number data during the past 400 years indicates that both the profile and the amplitude of the solar cycle have large variations. Some precursors of the solar cycle were identified aiming to predict the solar cycle. The polar field and the geomagnetic index are two precursors which are received the most attention. The geomagnetic variations during the solar minima are potentially caused by the solar polar field by the connection of the solar open flux. The robust prediction skill of the polar field indicates that the memory of the dynamo process is less than 11 yrs within the frame…
The correlation between geomagnetic activity and the sunspot number in the 11-year solar cycle exhibits long-term variations due to the varying time lag between the sunspot-related and non-sunspot related geomagnetic activity, and the varying relative amplitude of the respective geomagnetic activity peaks. As the sunspot-related and non-sunspot related geomagnetic activity are caused by different solar agents, related to the solar toroidal and poloidal fields, respectively, we use their variations to derive the parameters of the solar dynamo transforming the poloidal field into toroidal field …
