It has been recently suggested that white dwarfs generate magnetic fields in a process analogous to the Earth. The crystallization of the core creates a compositional inversion that drives convection, and combined with rotation, this can sustain a magnetic dynamo. We reanalyse the dynamo mechanism, arising from the slow crystallization of the core, and find convective turnover times $t_{\rm conv}$ of weeks to months - longer by orders of magnitude than previously thought. With white dwarf spin periods $P\ll t_{\rm conv}$, crystallization-driven dynamos are almost always in the fast rotating regime, where the magnetic field $B$ is at least in equipartition with the convective motion and is possibly further enhanced by a factor of $B\propto (t_{\rm conv}/P)^{1/2}$, depending on the assumed dynamo scaling law. We track the growth of the crystallized core using MESA and compute the magnetic field $B(T_{\rm eff})$ as a function of the white dwarf's effective temperature $T_{\rm eff}$. We compare this prediction with observations and show that crystallization-driven dynamos can explain some - but not all - of the $\sim$MG magnetic fields measured for single white dwarfs, as well as the stronger fields measured for white dwarfs in cataclysmic variables, which were spun up by mass accretion to short $P$. Our $B(T_{\rm eff})$ curves might also explain the clustering of white dwarfs with Balmer emission lines around $T_{\rm eff}\approx 7500\textrm{ K}$.
The mechanism of large-scale dynamos in rigidly rotating stratified convection is explored by direct numerical simulations (DNS) in Cartesian geometry. A mean-field dynamo model is also constructed using turbulent velocity profiles consistently extracted from the corresponding DNS results. By quantitative comparison between the DNS and our mean-field model, it is demonstrated that the oscillatory $α^2$ dynamo wave, excited and sustained in the convection zone, is responsible for large-scale magnetic activities such as cyclic polarity reversal and spatiotemporal migration. The results provide s…
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 …
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 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…
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…
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…
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…
In a rigidly-rotating magnetohydrodynamic (MHD) system with convective turbulence, a large-scale dynamo, categorized as the $α^2$-type, can be excited when the spin rate is large enough. In this paper, the rotational dependence of the $α^2$-type dynamo and the cause of it are explored by mean-field (MF) dynamo models coupled with direct numerical simulations (DNSs) of MHD convections. Bearing the application to the solar/stellar dynamo in mind, we adopt a strongly-stratified polytrope as a model of the convective atmosphere. Our DNS models show that the $α^2$-type dynamo is excited when ${\rm …
Main-sequence massive stars possess convective cores that likely harbor strong dynamo action. To assess the role of core convection in building magnetic fields within these stars, we employ the 3-D anelastic spherical harmonic (ASH) code to model turbulent dynamics within a 10 solar mass main-sequence (MS) B-type star rotating at 4 times the solar rate. We find that strong (900 kG) magnetic fields arise within the turbulence of the core and penetrate into the stably stratified radiative zone. These fields exhibit complex, time-dependent behavior including reversals in magnetic polarity and shi…
We report the finding of an azimuthal dynamo wave of a low-order (m=1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean field dynamo theory and have been obtained previously in mean-field models. Observational results both from photometry and Doppler imaging have revealed persistent drifts of spots for several rapidly rotating stars, but, although an azimuthal dynamo wave has been proposed as a possible mechanism responsible for this behavior, it has been judged as unlikely, as practical evidence for such waves from DNS ha…
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 …
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…
Several solar-like stars exhibit cyclic magnetic activity similar to the Sun as found in photospheric and chromospheric emission. We want to understand the physical mechanism involved in rotational dependence of these activity cycle periods. We use three-dimensional magnetohydrodynamical simulations of global convective dynamos models of solar-like stars to investigate the rotational dependency of dynamos. We further apply the test-field method to determine the $α$ effect in these simulations. We find dynamo with clear oscillating mean magnetic fields for moderately and rapidly rotating runs. …
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…
Spherical solar dynamo simulations are performed. Self-consistent, fully compressible magnetohydrodynamic system with a stably stratified layer below the convective envelope is numerically solved with a newly developed simulation code based on the Yin-Yang grid. The effects of penetrative convection are studied by comparing two models with and without the stable layer. The differential rotation profile in both models is reasonably solar-like with equatorial acceleration. When considering the penetrative convection, a tachocline-like shear layer is developed and maintained beneath the convectio…
A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We perform numerical simulations …
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…
We present the first global, three-dimensional simulations of solar/stellar convection that take into account the influence of magnetic flux emergence by means of the Babcock-Leighton (BL) mechanism. We have shown that the inclusion of a BL poloidal source term in a convection simulation can promote cyclic activity in an otherwise steady dynamo. Some cycle properties are reminiscent of solar observations, such as the equatorward propagation of toroidal flux near the base of the convection zone. However, the cycle period in this young sun (rotating three times faster than the solar rate) is ver…
Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandt…
Simple models of magnetic field generation by convection in rotating spherical shells exhibit properties resembling those observed on the sun. The {assumption of the Boussinesq approximation made in these models} prevents a realistic description of the solar cycle, but through a physically motivated change in the boundary condition for the differential rotation the propagation of dynamo waves towards higher latitudes can be reversed at least at low latitudes.
Betelgeuse is an M supergiant with a complex and extended atmosphere, which also harbors spots and giant granules at its surface. A possible magnetic field could contribute to the mass loss and to the heating of the outer atmosphere. We observed Betelgeuse, to directly study and infer the nature of its magnetic field. We used the new-generation spectropolarimeter NARVAL and the least square deconvolution (LSD) method to detect circular polarization within the photospheric absorption lines of Betelgeuse. We have unambiguously detected a weak Stokes V signal in the spectral lines of Betelgeuse, …
To understand the generation of the Earth's and planetary magnetic fields, we investigate numerically the combined effect of precession and convection on the dynamo action in a spherical shell. The convection alone, the precession alone and the combined effect of convection and precession are studied at the low Ekman number at which the precessing flow is already unstable. The key result is that although the precession or convection alone is not strong to support the dynamo action the combined effect of precession and convection can support the dynamo action because of the resonance of precess…
We have carried out numerical simulations of the convection zone in a K dwarf of 0.7 solar masses rotating at the solar rotation period. We study the convection pattern, the differential rotation and meridional flows, and the dynamo-generated magnetic field. We find that for a star of this type, the solar rotation period represents a case of fairly rapid rotation and the differential is solar-type. A dynamo-generated large scale field appears but it is neither dipolar nor does it show a simple activity cycle.
(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…
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.
We carry out high resolution calculations of the solar overshoot region with unprecedentedly realistic parameters, especially the small energy flux compared with $ρc^3_\mathrm{s}$, where $ρ$ and $c_\mathrm{s}$ are density and speed of sound. Our main purpose is to investigate behavior of the overshoot and the small-scale dynamo with parameters as close as possible to those of the Sun. Our calculations show that the bottom part of the convection zone becomes subadiabatic, which efficiently suppresses downflows. As a result we see a steep transition from the CZ to the RZ whose width is estimated…
Helioseismology shows that the regions occupied by convection and differential rotation inside the sun almost coincide. This supports the leading theoretical concept for the origin of differential rotation as a result of interaction between convection and rotation. This talk outlines the current state of the differential rotation theory. Numerical models based on the theory reproduce the observed solar rotation quite closely. The models also compute meridional flow and predict that the flow at the bottom of the convection zone is not small compared to the surface. Theoretical predictions for s…
M-dwarf stars are well known for the intense magnetic activity that many of them exhibit. In cool stars with near-surface convection zones, this magnetic activity is thought to be driven largely by the interplay of convection and the large scale differential rotation and circulations it establishes. The highly nonlinear nature of these flows yields a fascinatingly sensitive and diverse parameter space, with a wide range of possible dynamics. We report here on a set of three global MHD simulations of rapidly rotating M2 (0.4 $M_\odot$) stars. Each of these three models established nests of vigo…
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…
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,…
The global-scale dynamo action achieved in a simulation of a Sun-like star rotating at thrice the solar rate is assessed. The 3-D MHD Anelastic Spherical Harmonic (ASH) code, augmented with a viscosity minimization scheme, is employed to capture convection and dynamo processes in this G-type star. The simulation is carried out in a spherical shell that encompasses 3.8 density scale heights of the solar convection zone. It is found that dynamo action with a high degree of time variation occurs, with many periodic polarity reversals occurring roughly every 6.2 years. The magnetic energy also ris…
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…
We present results from compressible Cartesian convection simulations with and without imposed shear. In the former case the dynamo is expected to be of $α^2\varOmega$ type which is generally expected to be relevant for the Sun, whereas the latter case refers to $α^2$ dynamos which are more likely to occur in more rapidly rotating stars whose differential rotation is small. We perform a parameter study where the shear flow and the rotational influence are varied to probe the relative importance of both types of dynamos. Oscillatory solutions are preferred both in the kinematic and saturated re…
We investigate whether the recently suggested rotation and crystallization driven dynamo can explain the apparent increase of magnetism in old metal polluted white dwarfs. We find that the effective temperature distribution of polluted magnetic white dwarfs is in agreement with most/all of them having a crystallizing core and increased rotational velocities are expected due to accretion of planetary material which is evidenced by the metal absorption lines. We conclude that a rotation and crystallization driven dynamo offers not only an explanation for the different occurrence rates of strongl…
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…
We investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh-Bénard convection using direct numerical simulations. The kinetic and magnetic energies are divided into mean and turbulent components to study the production, transport, and dissipation associated with large and small-scale dynamos. This energy balance-based characterization reveals distinct mechanisms for large- and small-scale magnetic field generation in dynamos, depending on the nature of the velocity field and the conditions imposed at the boundaries.
We report the first successful simulation of spontaneous formation of surface magnetic structures from a large-scale dynamo by strongly-stratified thermal convection in Cartesian geometry. The large-scale dynamo observed in our strongly-stratified model has physical properties similar to those in earlier weakly-stratified convective dynamo simulations, indicating that the $α^2$-type mechanism is responsible for it. Additionally to the large-scale dynamo, we find that large-scale structures of the vertical magnetic field are spontaneously formed in the convection zone surface only for the case …
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.
We present a three-dimensional model of rotating convection combined with a simplified corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field that gets sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity.
Mean-field dynamo theory suggests that turbulent convection in a rotating layer of electrically-conducting fluid produces a significant alpha-effect, which is one of the key ingredients in any mean-field dynamo model. Provided that this alpha-effect operates more efficiently than (turbulent) magnetic diffusion, such a system should be capable of sustaining a large-scale dynamo. However, in the Boussinesq model that was considered by Cattaneo&Hughes (2006) the dynamo produced small-scale, intermittent magnetic fields with no significant large-scale component. In this paper, we consider the comp…
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…
Recent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of sign…
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…
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…
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…
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 …
We carry out non-rotating high-resolution calculations of the solar global convection, which resolve convective scales of less than 10 Mm. To cope with the low Mach number conditions in the lower convection zone, we use the reduced speed of sound technique (RSST), which is simple to implement and requires only local communication in the parallel computation. In addition, the RSST allows us to expand the computational domain upward to about $0.99 R_{\odot}$ as it can also handle compressible flows. Using this approach, we study the solar convection zone on the global scale, including small-scal…
