Connecting mean-field theory with dynamo simulations

\n Aims. We study turbulent transport coefficients that describe the evolution of\n large-scale magnetic fields in turbulent convection.\n Methods. We use the test field method, together with\n three-dimensional numerical simulations of turbulent convection\n with shear and rotation, to compute turbulent transport coefficients\n describing the evolution of large-scale magnetic fields in\n mean-field theory in the kinematic\n regime. We employ one-dimensional mean-field models with\n the derived turbulent transport coefficients to examine whether they\n give results that are compatible with direct simulations.\n Results. The results for the α-effect as a function of rotation rate are\n consistent with earlier numerical studies, i.e. increasing\n magnitude as rotation increases and approximately $\\cos \\theta$\n latitude profile for moderate rotation.\n Turbulent diffusivity, $\\eta_{\\rm t}$, is proportional to the square of the \n turbulent vertical velocity in all cases. Whereas $\\eta_{\\rm t}$ decreases \n approximately inversely proportional to the wavenumber of the field, \n the α-effect and turbulent pumping show a more complex behaviour \n with partial or full sign changes and the magnitude staying roughly \n constant.\n In the presence of shear and no rotation, a weak α-effect is induced which\n does not seem to show any consistent trend as a function of shear\n rate. Provided that the shear is large enough, this small\n α-effect is able to excite a dynamo in the mean-field\n model. The coefficient responsible for driving the shear-current\n effect shows several sign changes as a function of depth but is\n also able to contribute to dynamo action in the mean-field model. The\n growth rates in these cases are, however, well below those in\n direct simulations, suggesting that an incoherent α-shear\n dynamo may also act in the simulations.\n If both rotation and shear are present, the\n α-effect is more pronounced. \n At the same time, the combination\n of the shear-current and ${\\Omega}\\times{ J}$-effects is\n also stronger than in the case of shear alone, but subdominant to \n the α-shear dynamo. The\n results of direct simulations are consistent with mean-field models\n where all of these effects are taken into account without the\n need to invoke incoherent effects.\n

On the basis of the observations data the evolution of large-scale solar magnetic fields during three solar cycles was investigated and the general picture of changing the solar cycles of weak photospheric and strong (in active regions) fields was determined. It has been found that in addition to significant differences in the evolution of weak and strong magnetic fields there is a close relationship of their behavior in the separated out strength intervals, if the growth rate of the total flow field is considered as a characteristic for comparing. At present there is no well-reasoned theoretical explanation of the found in the article connection, and the problem of its interpretation is a subject of a separate research.

Conversion of gravitational energy into radiation near stars and compact objects in accretion disks and the origin of large-scale magnetic fields in astrophysical rotators have often been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large-scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disk theory have exemplified such ongoing pursuits. Twenty-first century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are really artificially separated pieces of what should ultimately be a single coupled theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large-scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small-scale magnetic fluctuations, without appealing to the traditional kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large-scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, it is important to study each disk hemisphere separately to avoid being potentially misled by the cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still play a fundamental role in large-scale dynamo action.

In the past two decades, the observed large-scale magnetic field of the active M dwarf star AD Leo has evolved from being strongly negative to mildly negative, raising a suspicion that it might be at the imminence of switching polarity (i.e. becoming positive). Although magnetic field reversals are observed every 11 years in the solar magnetic field, in the context of M dwarfs, magnetic field reversals are still poorly understood and so far not predictable. Further, no reversals have yet been observed for fast-rotating M dwarfs. Moreover, it is known that the magnetic field of stars impacts their surrounding space weather environment. Studying how space weather evolves over time is thus crucial for examining planetary habitability. We examine the properties of AD Leo's large-scale magnetic field, which was recently found to be trending towards a polarity reversal. We also investigate how the space weather environment changes in response to the evolution of the large-scale magnetic field, by modelling the wind of AD Leo. We analysed spectropolarimetric data collected by ESPaDOnS and SPIRou in late 2022 and early 2023. With the optical and near-infrared data we computed the longitudinal magnetic field, and with the near-infrared data we reconstructed the large-scale magnetic field using Zeeman-Doppler imaging. Using five magnetograms, from between 2019 and 2023, we simulated three-dimensional Alfvén wave-driven stellar winds using the state-of-the-art space weather code . SWMF Although we see an evolution of the large-scale magnetic field of AD Leo, we find no polarity reversal, but rather a restoration of the field to a simpler and axisymmetric configuration and consistently negative values for the longitudinal magnetic field strength. Previous work found the longitudinal field to get as weak as -46,G in 2020, and rather than continued weakening it now appears to be strengthening. Our new large-scale field reconstruction for AD Leo is characterised by a highly axisymmetric, poloidal-dipolar field with an increased mean large-scale field strength from 93,G to 145,G. However, the mean strength is still diminished compared to maps produced between 2007 and 2016. Our simulations of the space weather environment around AD Leo find the stellar mass loss rates to be on average -- an order of magnitude greater than the solar mass loss rate. Additionally, we examine the space weather experienced by hypothetical planets orbiting at the bounds of the habitable zone around AD Leo. We find that the entirety of the habitable zone resides beyond the Alfvén surface. Further, magnetised habitable zone planets (with planetary field strengths greater than 0.34,G) would likely be shielded from the incident wind and atmospheric erosion would be negligible (excluding effects from coronal mass ejections and flares). Additionally, we find the complexity of the wind velocity and wind pressure structures to evolve with the changing axisymmetry of the stellar large-scale magnetic field, resulting in more variable conditions along the orbits at certain epochs.

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 mechanism is robust to increasing stable stratification as long as the original requirements for its operation are met: a source of shear and non-helical magnetic fluctuations (e.g. from a small-scale dynamo). Both are plausibly sourced in the presence of differential rotation. Our idealized direct numerical simulations, supported by mean-field theory, demonstrate the generation of near equipartition large-scale toroidal fields. Additionally, a scan over magnetic Reynolds number shows no change in the growth or saturation of the LSD, providing good numerical evidence of a dynamo mechanism resilient to catastrophic quenching, which has been an issue for helical dynamos. These properties – the absence of catastrophic quenching and robustness to stable stratification – make the mechanism a plausible candidate for generating in situ large-scale magnetic fields in stellar radiative zones.

The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi‐analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha‐viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha‐accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A comprehensive approach is suggested for describing the origin and evolution of large-scale magnetic fields. Vorticity-dependent fluctuations acting on a primordial charged plasma account for field generation, and the properties of gauge-invariant (but conformally non-invariant) couplings of electromagnetic and gravitational fields in a FRW background are applied in order to supply a source-independent, gravity-driven mechanism of conductance induction in the course of the reheating phase of inflationary cosmic scenarios. In consequence, the description of the behaviour of large-scale primordial magnetic fields is complemented so as to cover the whole post-inflationary history of the universe.

Two spectral regimes of magnetic field amplification in magnetohydrodynamic (MHD) flows can be distinguished by the scale on which fields are amplified relative to the primary forcing scale of the turbulence. For field amplification at or below the forcing scale, the amplification can be called a “small-scale dynamo.” For amplification at and above the forcing scale the process can be called a “large-scale dynamo.” Non - local (in wave number) effects play a key role in both the growth of the small-scale field in non-helical turbulence and the growth of large and smallscale fields in helical turbulence. Mean field dynamo (MFD) theory represents a simple semi-analytic way to get a handle on large-scale field amplification in MHD turbulence. Helicity has long been known to be important for large scale, flux generating, externally forced MFDs. The extent to which such MFDs operate “slow” or “fast” (dependent or independent on magnetic Reynolds number) has been controversial, but there has been recent progress. Simulations of α2 dynamos in a periodic box dynamo and their quenching can now be largely understood within a simplified dynamical non-linear paradigm in which the MFD growth equation is supplemented by the total magnetic helicity evolution equation. For α2 dynamos, the large-scale field growth is directly related to the large-scale magnetic helicity growth. Magnetic helicity conservation then implies that growth of the large-scale magnetic helicity induces growth of small-scale magnetic (and current) helicity of the opposite sign, which eventually suppresses the α effect driving the MFD growth. Although the α2 MFD then becomes slow in the long time limit, substantial large-scale field growth proceeds in a kinematic, “fast” phase before non-linear asymptotic quenching of the “slow” phase applies. Ultimately, the MFD emerges as a process that transfers magnetic helicity between small and large scales. How these concepts apply to more general dynamos with shear, and open boundary dynamos is a topic of ongoing research. Some unresolved issues are identified. Overall, the following summarizes the most recent progress in mean-field dynamo theory: For a closed turbulent flow, the non-linear mean field dynamo, is first fast and kinematic, then slow and dynamic, and magnetic helicity transfer makes it so.KeywordsMagnetic EnergyMagnetic HelicityMagnetic Reynolds NumberDynamo TheoryForce ScaleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Convective dynamo simulations are performed in local Cartesian geometry. We report the first successful simulation of a large-scale oscillatory dynamo in rigidly rotating convection without stably stratified layers. A key requirement for exciting the large-scale dynamo is a sufficiently long integration time comparable to the ohmic diffusion time. By comparing two models with and without stably stratified layers, their effect on the large-scale dynamo is also studied. The spatiotemporal evolution of the large-scale magnetic field is similar in both models. However, it is intriguing that the magnetic cycle is much shorter in the model without the stable layer than with the stable layer. This suggests that the stable layer impedes the cyclic variations of the large-scale magnetic field.

Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arguments based on magnetic helicity conservation and a series of numerical simulations. Here we discuss recent efforts to explain fast magnetic reconnection through the topological effects of a weak stochastic magnetic field component. We also show how mean-field dynamo theory can be recast in a form which respects magnetic helicity conservation, and how this changes our understanding of astrophysical dynamos. Finally, we comment briefly on why an asymmetry between small scale magnetic and velocity fields is necessary for dynamo action, and how it can arise naturally.

We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding Universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early Universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early Universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding Universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields.

ABSTRACTSolar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, non-linear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence, and (iii) a convective turbulence. As the result of this effect, a non-linear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field αΩ, α2, and α2Ω dynamo instabilities are always saturated by the strong large-scale magnetic field.

The data obtained at the Routine Prediction Solar Telescope (RPST), which was designed and manufactured mainly at ISTP SB RAS and was installed at Kislovodsk MAS MAO RAN. The telescope is used to register weak large-scale fields throughout the solar disk with an angular resolution about 30 arcsec. The means square error of measurements is ~0.44 G in this case. The MAS MAO RPST observations have been compared with the magnetic fields and other solar activity parameters measured at different ground and space observatories. It was shown that the characteristics of the magnetic fields of active regions and largescale magnetic fields are interrelated. The evolution of the polar magnetic field was considered, and it was shown that the polarity in cycle 24 was reversed in June–July 2013 in the Northern Hemisphere and in December 2014–January 2015 in the Southern Hemisphere. At the same time, it has been noted that the magnetic field strength in the Northern Hemisphere at latitudes higher than 50° varied around zero in 2014, which indicates that the global field sign was reversed for a long time in the Northern Hemisphere.

Context. Most of the intracyclic variability in the large-scale solar magnetic field comes from the equatorial dipole component of the solar magnetic field. The equatorial dipole component is highly sensitive to the longitude distribution of the active regions. Aims. We quantify the effect of individual active regions on the large-scale solar magnetic field of the solar cycle 24. We study the effect of the longitude distribution of active regions on the strength of the large-scale dipole component. Methods. We used a surface flux transport (SFT) model to simulate the evolution of individual active regions and quantified their effect on the large-scale magnetic field using the recently developed vector sum method. We took advantage of the longitudinal translational invariance of the SFT model and compared the observed solar cycle 24 to the 10 000 simulations of the solar cycle 24 using randomized longitudinal source locations, but otherwise identical flux emergence. Results. We find that taking into account both the axial and equatorial components of the vector sum characterizing the global solar magnetic field sets better constraints on the parameter space of the SFT model than, for example, using the axial dipole moment alone as an optimization metric. We studied the maximum of cycle 24 and identified the recurrent and localized flux emergence in the southern hemisphere as the main culprit behind the rapid strengthening of the large-scale magnetic field in late 2014. We find that during the declining phase of the solar cycle, the strength of the large-scale magnetic field stayed above the median level of randomized simulations ( p < 0.027) for 42 subsequent rotations (from September 2014 to November 2017). This indicates that the longitudinal distribution of active regions is not random and, rather, that it demonstrates a tendency for some regions to emerge at longitudes where their equatorial components reinforce the large-scale equatorial field.

We present simulations of the 3D nonlinear induction equation in order to investigate the temporal evolution of large-scale magnetic fields in spiral galaxies. Our model includes differential rotation, ambipolar diffusion and, based on small-scale turbulence, eddy diffusivity and the tensorial α-effect with magnetic feedback. The nonaxisymmetric spiral pattern and – if considered – the vertical stratification of the galaxy are represented in its density and turbulence profile.