It is shown that the magnetic current-driven (`kink-type') instability produces flow and field patterns with helicity and even with α-effect but only if the magnetic background field possesses non-vanishing current helicity \bar{\vec{B}}\cdot curl \bar{\vec{B}} by itself. Fields with positive large-scale current helicity lead to negative small-scale kinetic helicity. The resulting α-effect is positive. These results are very strict for cylindric setups without <i>z/I>-dependence of the background fields. The sign rules also hold for the more complicated cases in spheres where the toroidal fields are the result of the action of differential rotation (induced from fossil poloidal fields) at least for the case that the global rotation is switched off after the onset of the instability.
When stars like our Sun are young they rotate rapidly and are very magnetically active. We explore dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. Wreath-building dynamos can undergo quasi-cyclic reversals of polarity and such behavior is common in the parameter space we have been able to explore. These dynamos do not appear to require tachoclines to achieve their spatial or temporal organization. Wreath-building d…
We investigate the effect of the surface bipolar magnetic regions (BMR) on the large-scale dynamo distributed in the bulk of the convection zone. The study employs the nonlinear 3D mean-field dynamo model. We model the emergence of the BMR on the surface through the nonaxisymmetric magnetic buoyancy effect, which acts on the large-scale toroidal magnetic field in the upper half of the convection zone. The nonaxisymmetric magnetic field which results from this mechanism is shallow. On the surface, the effect of the BMR on the magnetic field generation is dominant. {However, because of the shall…
We live near a magnetic star whose cycles of activity are driven by dynamo action beneath the surface. In the solar convection zone, rotation couples with plasma motions to build highly organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Despite our proximity to the Sun, the nature of its dynamo remains elusive, but observations of other solar-type stars show that surface magnetism is a nearly ubiquitous feature. In recent time, numerical simulations of convection and dynamo action have taken tremendous strides forward. Global-scale o…
Young solar-type stars rotate rapidly and are very magnetically active. The magnetic fields at their surfaces likely originate in their convective envelopes where convection and rotation can drive strong dynamo action. Here we explore simulations of global-scale stellar convection in rapidly rotating suns using the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. We explore one case rotates five times faster than the Sun in detail. This dynamo simulation, called …
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…
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…
We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated toward the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a s…
Parameters of magnetic activity on the solar type stars depend on the properties of the dynamo processes operating in stellar convection zones. We apply nonlinear mean-field axisymmetric $α^2Ω$ dynamo models to calculate of the magnetic cycle parameters, such as the dynamo cycle period, the total magnetic flux and the Poynting magnetic energy flux on the surface of solar analogs with the rotation periods from 15 to 30 days. The models take into account the principal nonlinear mechanisms of the large-scale dynamo, such as the magnetic helicity conservation, magnetic buoyancy, and effects of mag…
Torsional oscillations represent bands of fast and slow zonal flows around the Sun, which extend deep into the convection zone and migrate during solar cycles towards the equator following the sunspot butterfly diagram. Analysis of helioseismology data obtained in 1996-2018 for almost two solar cycles reveals zones of deceleration of the torsional oscillations inside the Sun due to dynamo-generated magnetic field. The zonal deceleration originates near the bottom of the convection zone at high latitudes, and migrates to the surface revealing patterns of magnetic dynamo waves predicted by the P…
The toroidal magnetic field is assumed to be generated in the tachocline in most Babcock-Leighton (BL)-type solar dynamo models, in which the poloidal field is produced by the emergence and subsequent dispersal of sunspot groups. However, magnetic activity of fully convective stars and MHD simulations of global stellar convection have recently raised serious doubts regarding the importance of the tachocline in the generation of the toroidal field. In this study, we aim to develop a new BL-type dynamo model, in which the dynamo operates mainly within the bulk of the convection zone. Our 2D mode…
We propose a solar dynamo model distributed in the bulk of the convection zone with the toroidal magnetic field the flux concentrated in the 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 closer to the surface, then the pattern of the modeled butterfly diagram for the toroidal magnetic fields in the upper part of the convection zone is formed by the surface rotational shear layer. The model is in agreement with observed properties of the magnetic solar cycle.
Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore,…
This paper considers a possibility of magnetic-field generation by local turbulent flows at the bottom of convective zone. The cycle of magnetic-field generation in this model can be represented in the form of sequency of processes. There are vortexes with azimuth axis, similar with Taylor vortex, close to the bottom of convection zone. This leads to the generation of twisted flux tubes because of screw dynamo. The growth of magnetic field causes emersion of U- loops. During the process of emersion and extraction azimuthal field of flux tubes converts to axial field, and reaches the surface as…
Our understanding of large-scale magnetic fields in stellar radiative zones remains fragmented and incomplete. Such magnetic fields, which must be produced by some form of dynamo mechanism, are thought to dominate angular-momentum transport, making them crucial to stellar evolution. A major difficulty is the effect of stable stratification, which generally suppresses dynamo action. We explore the effects of stable stratification on mean-field dynamo theory with a particular focus on a non-helical large-scale dynamo (LSD) mechanism known as the magnetic shear-current effect. We find that the me…
The interaction of helical convective motions and differential rotation in the solar convection zone results in turbulent drift of a large-scale magnetic field. We discuss the pumping mechanism and its impact on the solar dynamo.
The Sun and other cool stars harbouring outer convection zones manifest magnetic activity in their atmospheres. The connection between this activity and the properties of a deep-seated dynamo generating the magnetic flux is not well understood. By employing physical models, we study the spatial and temporal characteristics of the observable surface field for various stellar parameters. We combine models for magnetic flux generation, buoyancy instability, and transport, which encompass the entire convection zone. The model components are: (1) a thin-layer alpha-Omega dynamo at the base of the c…
Parker's analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity ("tachocline"), bounded by a perfect conductor ("radiative zone") on the one side, and by a highly diffusive medium ("convective zone") supporting an $α$-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rate and frequency of dynamo modes is analytically derived. Graphic solution of the dispersion relations displa…
Helioseismology provides important constraints for the solar dynamo problem. However, the basic properties and even the depth of the dynamo process, which operates also in other stars, are unknown. Most of the dynamo models suggest that the toroidal magnetic field that emerges on the surface and forms sunspots is generated near the bottom of the convection zone, in the tachocline. However, there is a number of theoretical and observational problems with justifying the deep-seated dynamo models. This leads to the idea that the subsurface angular velocity shear may play an important role in the …
Rotational shear layers at the boundary between radiative and convective zones, tachoclines, play a key role in the process of magnetic field generation in solar-like stars. We present two sets of global simulations of rotating turbulent convection and dynamo. The first set considers a stellar convective envelope only; the second one, aiming at the formation of a tachocline, considers also the upper part of the radiative zone. Our results indicate that the resulting mean-flows and dynamo properties like the growth rate, saturation energy and mode depend on the Rossby (Ro) number. For the first…
Obtaining observational evidence of the turbulent component of solar dynamo operating in the convective zone is a challenging problem because the dynamo action is hidden below the photosphere. Here we present results of a statistical study of flaring active regions (ARs) that produced strong solar flares of an X-ray class X1.0 and higher during a time period that covered solar cycles 23 and 24. We introduced a magneto-morphological classification (MMC) of ARs, which allowed us to estimate possible contribution of the turbulent component of the dynamo into the structure of an AR. We found that …
We extend earlier models of turbulent dynamos with an upper, nearly force-free exterior to spherical geometry, and study how flux emerges from lower layers to the upper ones without being driven by magnetic buoyancy. We also study how this affects the possibility of plasmoid ejection. A spherical wedge is used that includes northern and southern hemispheres up to mid-latitudes and a certain range in longitude of the Sun. In radius, we cover both the region that corresponds to the convection zone in the Sun and the immediate exterior up to twice the radius of the Sun. Turbulence is driven with …
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…
We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small--scale field is transported outwards and form large structures like magnetic clouds.
The first results of the solar dynamo model that allows for the diamagnetic effect of inhomogeneous turbulence and the nonlocal alpha-effect due to the rise of magnetic loops are discussed. The nonlocal alpha-effect is not subject to the catastrophic quenching related to the conservation of magnetic helicity. Given the diamagnetic pumping, the magnetic fields are concentrated near the base of the convection zone, although the distributed-type model covers the entire thickness of the convection zone. The magnetic cycle period, the equatorial symmetry of the field, its meridional drift, and the …
A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3-D, global solar simulation in which a tachocline is confined by a self-excited dynamo. The non-axisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that arise from equatoria…
We propose a phenomenological technique for modelling the emergence of active regions within a three-dimensional, kinematic dynamo framework. By imposing localised velocity perturbations, we create emergent flux-tubes out of toroidal magnetic field at the base of the convection zone, leading to the eruption of active regions at the solar surface. The velocity perturbations are calibrated to reproduce observed active region properties (including the size and flux of active regions, and the distribution of tilt angle with latitude), resulting in a more consistent treatment of flux-tube emergence…
We investigate the emergence of a large-scale magnetic field. This field is dynamo-generated by turbulence driven with a helical forcing function. Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Time series of the magnetic field structure show recurrent plasmoid ejections.
Transport of angular momentum and chemical elements by the MRI dynamo in stellar radiative zones
Toulouse Univ.（图卢兹大学）；Institut de Recherche en Astrophysique et Planétologie（天体物理学与行星学研究所在）；CNRS（法国国家科学研究中心）；CNES（法国国家空间研究中心）；Département d’Astrophysique/AIM CEA/IRFU（天体物理系/AIM cea/IRFU）；Univ. Paris-Saclay（巴黎萨克雷大学）；Univ. de Paris Cité（巴黎西岱大学）；Institut de Mécanique des Fluides de Toulouse（图卢兹流体力学研究所）
Coexisting Tayler instability-driven dynamos in radiative zones: New dynamo solution and its impacts on stellar physics
Université de Genève（日内瓦大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；IRAP, Université de Toulouse, CNRS, CNES, UPS（图卢兹大学 IRAP 研究所）；Institut Universitaire de France (IUF)（法国高等研究院）
Solar dynamo models require some mechanism for magnetic field concentration near the base of the convection zone in order to generate super-kilogauss toroidal fields with sufficiently large (~10^{24} Mx) magnetic flux. We consider the downward diamagnetic pumping near the base of the convection zone as a possible concentration mechanism and derive the pumping velocities with allowance for the effect of rotation. Transport velocities for poloidal and toroidal fields differ in rotating fluid. The toroidal field is transported downward along the radius only but the pumping velocity for the poloid…
The meridional circulation of the Sun, which is observed to be poleward at the surface, should have a return flow at some depth. Since large-scale flows like the differential rotation and the meridional circulation are driven by turbulent stresses in the convection zone, these flows are expected to remain confined within this zone. Current observational (based on helioseismology) and theoretical (based on dynamo theory) evidences point towards an equatorward return flow of the meridional circulation at the bottom of the convection zone. Assuming the mean values of various quantities averaged o…
We study the connections between the sun's convection zone and the evolution of the solar wind and corona. We let the magnetic fields generated by a 2.5D axisymmetric kinematic dynamo code (STELEM) evolve in a 2.5D axisymmetric coronal isothermal MHD code (DIP). The computations cover an 11 year activity cycle. The solar wind's asymptotic velocity varies in latitude and in time in good agreement with the available observations. The magnetic polarity reversal happens at different paces at different coronal heights. Overall sun's mass loss rate, momentum flux and magnetic braking torque vary con…
Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independe…
We carry out high-resolution calculations for the stellar convection zone. The main purpose of this study is to investigate the effect of a small-scale dynamo on the differential rotation. The solar differential rotation deviates from the Taylor-Proudman state in which the angular velocity does not change along the rotational axis. To break the Taylor-Proudman state deep in the convection zone, it is thought that a latitudinal entropy gradient is required. In this study, we find that the small-scale dynamo has three roles in the deviation of the stellar differential rotation from the Taylor-Pr…
Context: The Sun's polar fields and open flux around the time of activity minima have been considered to be strongly correlated with the strength of the subsequent maximum of solar activity. Aims: We aim to investigate the behavior of a Babcock-Leighton dynamo with a source poloidal term that is based on the observed sunspot areas and tilts. In particular, we investigate whether the toroidal fields at the base of convection zone from the model are correlated with the observed solar cycle activity maxima. Methods: We used a flux transport dynamo model that includes convective pumping and a polo…
The sunspot cycle is the magnetic cycle of the Sun produced by the dynamo process. A central idea of the solar dynamo is that the toroidal and the poloidal magnetic fields of the Sun sustain each other. We discuss the relevant observational data both for sunspots (which are manifestations of the toroidal field) and for the poloidal field of the Sun. We point out how the differential rotation of the Sun stretches out the poloidal field to produce the toroidal field primarily at the bottom of the convection zone, from where parts of this toroidal field may rise due to magnetic buoyancy to produc…
When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for a system rotating at three times the current solar rotation rate. We find that substantial organized global-scale magnet…
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 …
We present photometric spot modeling of the nearly four-year long light-curve of the Kepler target KIC 5955122 in terms of persisting dark circular surface features. With a Bayesian technique, we produced a plausible surface map that shows dozens of small spots. After some artifacts are removed, the residuals are at $\pm 0.16$\,mmag. The shortest rotational period found is $P = 16.4 \pm 0.2$ days. The equator-to-pole extrapolated differential rotation is $0.25 \pm 0.02$ rad/d. The spots are roughly half as bright as the unperturbed stellar photosphere. Spot latitudes are restricted to the zone…
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 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…
The phenomenon of solar "torsional oscillations" (TO) represents migratory zonal flows associated with the solar cycle. These flows are observed on the solar surface and, according to helioseismology, extend through the convection zone. We study the origin of the TO using results from a global MHD simulation of the solar interior that reproduces several of the observed characteristics of the mean-flows and magnetic fields. Our results indicate that the magnetic tension (MT) in the tachocline region is a key factor for the periodic changes in the angular momentum transport that causes the TO. T…
Helicity and αeffect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates producing a net kinetic helicity anticorrelated to the current helicity of the background field. The mean electromotive force is computed with the result that the…
We investigate the relations between tachocline-based dynamos and the surface flux transport mechanisms in stars with outer convection zones. Using our combined models of flux generation and transport, we demonstrate the importance of the buoyant rise of magnetic flux, which physically determines the emergence latitudes and tilt angles of bipolar magnetic regions. The combined effects of the dynamo strength, flux rise, and surface transport lead to various cyclic and non-cyclic time series of total unsigned surface magnetic flux.
The Kepler mission has collected light curves for almost 4 years. The excellent quality of these data has allowed us to probe the structure and the dynamics of the stars using asteroseismology. With the length of data available, we can start to look for magnetic activity cycles. The Kepler data obtained for the F star, KIC 12009504, shows a rotation period of 9.5 days and additional variability that could be due to the magnetic activity of the star. Here we present recent and preliminary 3D global-scale dynamo simulations of this star with the ASH and STELEM codes, capturing a substantial port…
To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the con…
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 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 …
When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for two systems, rotating at three and five times the current solar rate. We find that substantial organized global-scale ma…
We present numerical investigations into three principal properties of the small-scale dynamo in stably stratified turbulence: the onset criterion, the growth rate, and the nature of the magnetic field anisotropy in the kinematic regime. The results suggest that all three dynamo properties are controlled by the scale separation between the Ozmidov scale and the viscous or resistive scale. In addition to the critical magnetic Reynolds number, this allows for the definition of critical buoyancy and magnetic buoyancy Reynolds numbers for stratified small-scale dynamo onset in the high and low mag…
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 …
