Flux-dominated solar dynamo model with a thin shear layer

Flux-dominated solar dynamo models have demonstrated to reproduce the main features of the large scale solar magnetic cycle, however the use of a solar like differential rotation profile implies in the the formation of strong toroidal magnetic fields at high latitudes where they are not observed. In this work, we invoke the hypothesis of a thin-width tachocline in order to confine the high-latitude toroidal magnetic fields to a small area below the overshoot layer, thus avoiding its influence on a Babcock-Leighton type dynamo process. Our results favor a dynamo operating inside the convection zone with a tachocline that essentially works as a storage region when it coincides with the overshoot layer. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Connection Between Mean Field Dynamo Theory and Flux Tubes

Mean field dynamo theory deals with various mean quantities and does not directly throw any light on the question of existence of flux tubes. We can, however, draw important conclusions about flux tubes in the interior of the Sun by combining additional arguments with the insights gained from solar dynamo solutions. The polar magnetic field of the Sun is of order 10 G, whereas the toroidal magnetic field at the bottom of the convection zone has been estimated to be 100000 G. Simple order-of-magnitude estimates show that the shear in the tachocline is not sufficient to stretch a 10 G mean radial field into a 100000 G mean toroidal field. We argue that the polar field of the Sun must get concentrated into intermittent flux tubes before it is advected to the tachocline. We estimate the strengths and filling factors of these flux tubes. Stretching by shear in the tachocline is then expected to produce a highly intermittent magnetic configuration at the bottom of the convection zone. The meridional flow at the bottom of the convection zone should be able to carry this intermittent magnetic field equatorward, as suggested recently by Nandy and Choudhuri (2002). When a flux tube from the bottom of the convection zone rises to a region of pre-existing poloidal field at the surface, we point out that it picks up a twist in accordance with the observations of current helicities at the solar surface.     

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.     

Fluctuations of the Solar Dynamo Observed in the Solar Wind and Interplanetary Magnetic Field at 1 AU and in the Outer Heliosphere

Recent helioseismic observations have found strong fluctuations at a period of about 1.3 years in the rotation speed around the tachocline in the deep solar convection layer. Similar mid-term quasi-periodicities (MTQP; periods between 1–2 years) are known to occur in various solar atmospheric and heliospheric parameters for centuries. Since the deep convection layer is the expected location of the solar magnetic dynamo, its fluctuations could modulate magnetic flux generation and cause related MTQP fluctuations at the solar surface and beyond. Accordingly, it is likely that the heliospheric MTQP periodicities reflect similar changes in solar dynamo activity. Here we study the occurrence of the MTQP periodicities in the near and distant heliosphere in the solar wind speed and interplanetary magnetic field observed by several satellites at 1 AU and by four interplanetary probes (Pioneer 10 and 11 and Voyager 1 and 2) in the outer heliosphere. The overall structure of MTQP fluctuations in the different locations of the heliosphere is very consistent, verifying the solar (not heliospheric) origin of these periodicities. We find that the mid-term periodicities were particularly strong during solar cycle 22 and were observed at two different periods of 1.3 and 1.7 years simultaneously. These periodicities were latitudinally organized so that the 1.3-year periodicity was found in solar wind speed at low latitudes and the 1.7-year periodicity in IMF intensity at mid-latitudes. While all heliospheric results on the 1.3-year periodicity are in a good agreement with helioseismic observations, the 1.7-year periodicity has so far not been detected in helioseismic observations. This may be due to temporal changes or due to the helioseismic method where hemispherically antisymmetric fluctuations would so far have remained hidden. In fact, there is evidence that MTQP fluctuations may occur antisymmetrically in the northern and southern solar hemisphere. Moreover, we note that the MTQP pattern was quite different during solar cycles 21 and 22, implying fundamental differences in solar dynamo action between the two halves of the magnetic cycle.     

The Kinematic Theory of Solar Dynamo

Generation of the Sun‘s magnetic fields by self-inductive processes in the solar electrically conducting interior, the solar dynamo theory, is a fundamentally important subject in astrophysics. The kinematic dynamo theory concerns how the magnetic fields are produced by kinematically possible flows without being constrained by the dynamic equation. We review a number of basic aspects of the kinematic dynamo theory, including the magnetohydrodynamic approximation for the dynamo equation, the impossibility of dynamo action with the solar differential rotation, the Cowling‘s anti-dynamo theorem in the solar context, the turbulent alpha effect and recently constructed three-dimensional interface dynamos controlled by the solar tachocline at the base of the convection zone.     

An Exploration of Non-kinematic Effects in Flux Transport Dynamos

Recent global magnetohydrodynamical simulations of solar convection producing a large-scale magnetic field undergoing regular, solar-like polarity reversals also present related cyclic modulations of large-scale flows developing in the convecting layers. Examination of these simulations reveal that the meridional flow, a crucial element in flux transport dynamos, is driven at least in part by the Lorentz force associated with the cycling large-scale magnetic field. This suggests that the backreaction of the field onto the flow may have a pronounced influence on the long-term evolution of the dynamo. We explore some of the associated dynamics using a low-order dynamo model that includes this Lorentz force feedback. We identify several characteristic solutions which include single period cycles, period doubling and chaos. To emulate the role of turbulence in the backreaction process we subject the model to stochastic fluctuations in the parameter that controls the Lorentz force amplitude. We find that short term fluctuations produce long-term modulations of the solar cycle and, in some cases, grand minima episodes where the amplitude of the magnetic field decays to near zero. The chain of events that triggers these quiescent phases is identified. A subsequent analysis of the energy transfer between large-scale fields and flows in the global magnetohydrodynamical simulation of solar convection shows that the magnetic field extracts energy from the solar differential rotation and deposits part of that energy into the meridional flow. The potential consequences of this marked departure from the kinematic regime are discussed in the context of current solar cycle modeling efforts based on flux transport dynamos.     

On the interaction between differential rotation and magnetic fields in the Sun

We have performed 3-D numerical simulations of compressible convection under the influence of rotation and magnetic fields in spherical shells. They aim at understanding the subtle coupling between convection, rotation and magnetic fields in the solar convection zone. We show that as the magnetic Reynolds number is increased in the simulations, the magnetic energy saturates via nonlinear dynamo action, to a value smaller but comparable to the kinetic energy contained in the shell, leading to increasingly strong Maxwell stresses that tend to weaken the differential rotation driven by the convection. These simulations also indicate that the mean toroidal and poloidal magnetic fields are small compared to their fluctuating counterparts, most of the magnetic energy being contained in the non-axisymmetric fields. The intermittent nature of the magnetic fields generated by such a turbulent convective dynamo confirms that in the Sun the large-scale ordered dynamo responsible for the 22-year cycle of activity can hardly be located in the solar convective envelope.     

Mechanism of cyclically polarity reversing solar magnetic cycle as a cosmic dynamo

We briefly describe historical development of the concept of solar dynamo mechanism that generates electric current and magnetic field by plasma flows inside the solar convection zone. The dynamo is the driver of the cyclically polarity reversing solar magnetic cycle. The reversal process can easily and visually be understood in terms of magnetic field line stretching and twisting and folding in three-dimensional space by plasma flows of differential rotation and global convection under influence of Coriolis force. This process gives rise to formation of a series of huge magnetic flux tubes that propagate along iso-rotation surfaces inside the convection zone. Each of these flux tubes produces one solar cycle. We discuss general characteristics of any plasma flows that can generate magnetic field and reverse the polarity of the magnetic field in a rotating body in the Universe. We also mention a list of problems which are currently being disputed concerning the solar dynamo mechanism together with observational evidences that are to be constraints as well as verifications of any solar cycle dynamo theories of short and long term behaviors of the Sun, particularly time variations of its magnetic field, plasma flows, and luminosity.     

The solar dynamo

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.Received: 5 May 2003, Published online: 15 July 2003     

HALF-WIDTH OF A SOLAR DYNAMO WAVE IN PARKER'S MIGRATORY DYNAMO

A kinematic -dynamo model of magnetic field generation in a thin convection shell with nonuniform helicity for large dynamo numbers is considered in the framework of Parker's migratory dynamo. The asymptotic solution obtained of equations governing the magnetic field has the form of an anharmonic travelling dynamo wave. This wave propagates over most latitudes of the solar hemisphere from high latitudes to the equator, and the amplitude of the magnetic field first increases and then decreases with propagation. Over the subpolar latitudes, the dynamo wave reverses; there the dynamo wave propagates polewards and decays with latitude. The half-width of the maximum of the magnetic field localisation and the phase velocity of the dynamo wave are calculated. Butterfly diagrams are plotted and analysed and these show that even a simple model may reveal some properties of the solar magnetic fields.     

Fluid Dynamics and MHD of the Solar Convection Zone and Tachocline: Current Understanding and Unsolved Problems – (Invited Review)

We review recent progress and define unanswered scientific questions in five related topics: granulation- to supergranulation-scale convection and magnetic structures; global convection and circulation; the rise of magnetic flux tubes to the photosphere, and their injection into the base of the convection zone; tachocline fluid dynamics and MHD; and the solar dynamo. We close with a set of observational `targets' for helioseismologists to aim for.     

Electric current helicity in the solar atmosphere

In the theories of solar magnetism, kinetic and magnetic helicities, which arise as a consequence of the rotation of the Sun, play a key role. The dynamo for the main field is assumed to operate in the convection zone. The solar rotation also may be the ultimate cause for the generation of dc electric currents in the atmosphere, needed as the energy source for flares. Then in the atmosphere the electric current helicity, H _C = B · × B, which is a pseudo-scalar quantity, should be antisymmetric about the equatorial plane. An inspection of 16 active regions, for which H _C has been estimated by using extrapolation of measured photospheric magnetic fields, leads to the result that the electric current helicity is predominantly negative in the northern and positive in the southern hemisphere. The helicity of the large-scale currents generated according to standard dynamo theory by the alpha effect in the convection zone is just opposite in sign. Current generation due to rotational motions of sunspots and other magnetic elements in accordance with the global differential rotation, i.e., counter-clockwise in the northern and clockwise in the southern hemisphere, however, can explain the rule found. Also in some alternative dynamo models for the global field, in which the dynamo operates at the base of the convection zone, the large-scale current helicity generated by the alpha effect has the sign needed.     

Dynamo action in the presence of an imposed magnetic field

Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An unconventional accretion disc dynamo

In the light of recent results from numerical simulations of accretion disc MHD turbulence, we revisit the problem of the configuration of large-scale magnetic fields resulting from an α Ω dynamo operating in a thin accretion disc. In particular, we analyse the consequences of the peculiar sign of the α -effect suggested by numerical simulations . We determine the symmetry of the fastest-growing modes in the kinematic dynamo approximation and, in the framework of an ' α -quenched' dynamo model, study the evolution of the magnetic field. We find that the resulting field for this negative polarity of the α -effect generally has dipole symmetry with respect to the disc midplane, although the existence of an equilibrium configuration depends on the properties of the turbulence. The role of magnetic field dragging is discussed and, finally, the presence of an external uniform magnetic field is included to address the issue of magneto centrifugal wind launching from accretion discs.     

Dynamo saturation in direct simulations of the multi‐phase turbulent interstellar medium

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean‐field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical‐flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean‐field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three‐dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing‐periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean‐field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched α) dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub‐grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solar cycle general magnetic fields of 1959–1974 and dynamical structure of the convection zone

The concept of the solar general magnetic field is extended from that of the polar fields to the concept of any axisymmetric fields of the whole Sun. The poloidal and toroidal general magnetic fields are defined and diagrams of their evolutionary patterns are drawn using the Mount Wilson magnetic synoptic chart data of Carrington rotation numbers from 1417 to 1620 covering approximately half of cycle 19 and cycle 20. After averaging over many rotations long-term regularities appear in the patterns. The diagrams of the patterns are compared with the Butterfly Diagram of sunspots of the same period. The diagram of the poloidal field shows that the Sun behaves like a magnetic quadrupole, each hemisphere having two branches of opposite polarities with mirror images on the other hemisphere. This was predicted by a solar cycle model driven by the dynamo action of the global convection by Yoshimura and could serve as a verification of the model. The diagram of the toriodal field is similar to the Butterfly Diagram of sunspots. The slight differences which do exist between the two diagrams seems to show that the fields responsible for the two may originate from different zones of the Sun. Common or different characteristics of the three diagrams are examined in terms of dynamical structure of the convection zone referring to the theoretical model of the solar cycle driven by the dynamo action of the global convection.     

Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone

In order to extend the abilities of the αΩ dynamo model to explain the observed regularities and anomalies of the solar magnetic activity, the negative buoyancy phenomenon and the magnetic quenching of the α effect were included in the model, as well as newest helioseismically determined inner rotation of the Sun were used. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the solar convection zone (SCZ). Therefore, we examined two “antibuoyancy” effects: i) macroscopic turbulent diamagnetism and ii) magnetic advection caused by vertical inhomogeneity of fluid density in the SCZ, which we call the ∇ρ effect. The Sun's rotation substantially modifies the ∇ρ effect. The reconstruction of the toroidal field was examined assuming the balance between mean‐field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. It is shown that at high latitudes antibuoyancy effects block the magnetic fields in the deep layers of the SCZ, and so the most likely these deep‐rooted fields could not become apparent at the surface as sunspots. In the near‐equatorial region, however, the upward ∇ρ effect can facilitate magnetic fields of about 3000 – 4000 G to emerge through the surface at the sunspot belt. Allowance for the radial inhomogeneity of turbulent velocity in derivations of the helicity parameter resulted in a change of sign of the α effect from positive to negative in the northern hemisphere near the bottom of the SCZ. The change of sign is very important for direction of the Parker's dynamo‐waves propagation and for parity of excited magnetic fields. The period of the dynamo‐wave calculated with allowance for the magnetic quenching is about seven years, that agrees by order of magnitude with the observed mean duration of the sunspot cycles. Using the modern helioseismology data to define dynamo‐parameters, we conclude that north‐south asymmetry should exist in the meridional field. At low latitudes in deep layers of the SCZ, the αΩ dynamo excites most efficiency the dipolar mode of the meridional field. Meanwhile, in high‐latitude regions a quadrupolar mode dominates in the meridional field. The obtained configuration of the net meridional field is likely to explain the magnetic anomaly of polar fields (the apparent magnetic “monopole”) observed near the maxima of solar cycles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some recent developments in solar dynamo theory

We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock-Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well.     

On the possibility of a bimodal solar dynamo

A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analogous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4–5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meridional circulation and the period of the solar dynamo cycle

We consider the conditions in the transition from the tachocline to the solar convective zone with changing diffusion coefficient. The topology of the magnetic fields involved in the solar dynamo is revised under the assumption that intermediate fields (of the order of 10 mT) have a dominant role in generating the fields in new cycle. The inclusion of meridional circulation is found to increase the dynamo wave period in comparison to the observed period. This suggests that the αΩ-effects are unimportant in calculating the solar cycle period but hold significance in determining the cycle amplitude.