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The initial magnetic field of previous magnetorotational instability (MRI) simulations has always included a significant system-scale component, even if stochastic. However, it is of conceptual and practical interest to assess whether the MRI can grow when the initial field is turbulent. The ubiquitous presence of turbulent or random flows in astrophysical plasmas generically leads to a small-scale dynamo (SSD), which would provide initial seed turbulent velocity and magnetic fields in the plasma that becomes an accretion disc. Can the MRI grow from these more realistic initial conditions? To address this, we supply a standard shearing box with isotropically forced SSD generated magnetic and velocity fields as initial conditions and remove the forcing. We find that if the initially supplied fields are too weak or too incoherent, they decay from the initial turbulent cascade faster than they can grow via the MRI. When the initially supplied fields are sufficient to allow MRI growth and sustenance, the saturated stresses, large-scale fields and power spectra match those of the standard zero net flux MRI simulation with an initial large-scale vertical field. [ABSTRACT FROM AUTHOR]

Magnetic dynamo action caused by themagnetorotational instability is studied in the shearingbox approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disc plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale non-zero azimuthal magnetic fluxes, facilitating the instability. In agreement with this picture, the cases when the dynamo is efficient are characterized by a strong intermittency of the local azimuthal magnetic fluxes. [ABSTRACT FROM AUTHOR]

We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parametrized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the ‘no-z’ approximation and the dynamical α-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted on to galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure data sets. Further, we explore the properties of our numerical solutions, and their dependence on certain parameter values. We illustrate and assess the degree to which numerical solutions based on various levels of approximation, common in the dynamo literature, agree with one another. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution ofWolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behaviour of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 yr ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 per cent correlation over all intervals of observation (about 270 yr). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependences are in good agreement with observations. [ABSTRACT FROM AUTHOR]

Recent data on superflares on Sun-like stars and radiocarbon data on solar activity in the past are both indicative of transient epochs of unusually high magnetic activity. We propose an explanation for the grand activity maxima in the framework of a solar dynamo model with fluctuating parameters. Solar-type dynamos are oscillatory because of the combination of the solar-type differential rotation with positive (in the Northern hemisphere) alpha-effect. An artificial reversal of the sign in the alpha-effect changes the dynamo to a steady regime with hundreds of times larger magnetic energy compared to the amplitude of the cyclic dynamo. Sufficiently large and durable fluctuations reversing the sign of the alpha-effect during the growth phase of a magnetic cycle can, therefore, cause a transient change to a steady dynamo with considerably increased magnetic energy. This qualitative scenario for grand activity maxima is supported by computations of the dynamo model with a fluctuating alpha-effect. The computed statistics of several thousand magnetic cycles gives examples of cycles with very high magnetic energy. Our preliminary estimations, however, suggest that the probability of solar superflares is extremely low. [ABSTRACT FROM AUTHOR]

Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. Aims. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular, with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Methods. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. Results. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings. [ABSTRACT FROM AUTHOR]

Context. The large-scale magnetic field in the Sun varies with a period of approximately 22 years, although the amplitude of the cycle is subject to long-term modulation with recurrent phases of significantly reduced magnetic activity. It is believed that a hydromagnetic dynamo is responsible for producing this large-scale field, although this dynamo process is not well understood. Aims. Within the framework of mean-field dynamo theory, our aim is to investigate how competing mechanisms for poloidal field regeneration (namely a time-delayed Babcock-Leighton surface α-effect and an interface-type α-effect), can lead to the modulation of magnetic activity in a deep-seated solar dynamo model. Methods. We solve the standard αΩ dynamo equations in one spatial dimension, including source terms corresponding to both of the competing α-effects in the evolution equation for the poloidal field. This system is solved using two different methods. In addition to solving the one-dimensional partial differential equations directly, using numerical techniques, we also use a local approximation to reduce the governing equations to a set of coupled ordinary differential equations (ODEs), which are studied using a combination of analytical and numerical methods. Results. In the ODE model, it is straightforward to find parameters such that a series of bifurcations can be identified as the time delay is increased, with the dynamo transitioning from periodic states to chaotic states via multiply periodic solutions. Similar transitions can be observed in the full model, with the chaotically modulated solutions exhibiting solar-like behaviour. Conclusions. Competing α-effects could explain the observed modulation in the solar cycle. [ABSTRACT FROM AUTHOR]

Aims. The Sun shows strong variability in its magnetic activity, from Grand minima to Grand maxima, but the nature of the variability is not fully understood, mostly because of the insufficient length of the directly observed solar activity records and of uncertainties related to long-term reconstructions. Here we present a new adjustment-free reconstruction of solar activity over three millennia and study its different modes. Methods. We present a new adjustment-free, physical reconstruction of solar activity over the past three millennia, using the latest verified carbon cycle, 14C production, and archeomagnetic field models. This great improvement allowed us to study different modes of solar activity at an unprecedented level of details. Results. The distribution of solar activity is clearly bi-modal, implying the existence of distinct modes of activity. The main regular activity mode corresponds to moderate activity that varies in a relatively narrow band between sunspot numbers 20 and 67. The existence of a separate Grand minimum mode with reduced solar activity, which cannot be explained by random fluctuations of the regular mode, is confirmed at a high confidence level. The possible existence of a separate Grand maximum mode is also suggested, but the statistics is too low to reach a confident conclusion. Conclusions. The Sun is shown to operate in distinct modes - a main general mode, a Grand minimum mode corresponding to an inactive Sun, and a possible Grand maximum mode corresponding to an unusually active Sun. These results provide important constraints for both dynamo models of Sun-like stars and investigations of possible solar influence on Earth's climate. [ABSTRACT FROM AUTHOR]

Context. Star-forming dwarf galaxies can be seen as the local proxies of the high-redshift building blocks of more massive galaxies according to the current paradigm of the hierarchical galaxy formation. They are low-mass objects, and therefore their rotation speed is very low. Several galaxies are observed to show quite strong magnetic fields. These cases of strong ordered magnetic fields seem to correlate with a high, but not extremely high, star formation rate. Aims. We investigate whether these magnetic fields could be generated by the cosmic-ray-driven dynamo. The environment of a dwarf galaxy is unfavourable for the large-scale dynamo action because of the very slow rotation that is required to create the regular component of the magnetic field. Methods. We built a 3D global model of a dwarf galaxy that consists of two gravitational components: the stars and the dark-matter halo described by the purely phenomenological profile proposed previously. We solved a system of magnetohydrodynamic equations that include an additional cosmic-ray component described by the fluid approximation. Results. We found that the cosmic-ray-driven dynamo can amplify the magnetic field with an exponential growth rate. The e-folding time is correlated with the initial rotation speed. The final mean value of the azimuthal flux for our models is on the order of few μG and the system reaches its equipartition level. The results indicate that the cosmic-ray-driven dynamo is a process that can explain the magnetic fields in dwarf galaxies. [ABSTRACT FROM AUTHOR]

Context. Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field can now be modelled with an unprecedented level of detail and complexity. Aims. We aim to complement this phenomenological approach with a physically motivated, quantitative dynamo model - a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc. Methods. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we performed three-dimensional global simulations of the Galactic disc. To eliminate free parameters, closure coefficients embodying the mean-field dynamo were calibrated against resolved local simulations of supernova-driven interstellar turbulence. Results. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode with even parity, and a subdominant A0 mode with odd parity. Notably, this superposition of modes creates a strong localised vertical field on one side of the Galactic disc. Moreover, we found significant radial pitch angles that decay with radius, which can be explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the calmer outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for a mean-field dynamo alone) to about 10 kpc in the hybrid models - the latter being in much better agreement with observations. Conclusions. There remain aspects (e.g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, we demonstrate that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts. [ABSTRACT FROM AUTHOR]

We investigate the saturation level of hydromagnetic turbulence driven by the magnetorotational instability in the case of vanishing net flux. Motivated by a recent paper of Bodo et al., we here focus on the case of a non-isothermal equation of state with constant thermal diffusivity. The central aim of the paper is to complement the previous result with closure parameters for mean-field dynamo models, and to test the hypothesis that the dynamo is affected by the mode of heat transport. We perform computer simulations of local shearing-box models of stratified accretion disks with approximate treatment of radiative heat transport, which is modeled via thermal conduction. We study the effect of varying the (constant) thermal diffusivity, and apply different vertical boundary conditions (BCs). In the case of impenetrable vertical boundaries, we confirm the transition from mainly conductive to mainly convective vertical heat transport below a critical thermal diffusivity. This transition is however much less dramatic when more natural outflow BCs are applied. Similarly, the enhancement of magnetic activity in this case is less pronounced. Nevertheless, heating via turbulent dissipation determines the thermodynamic structure of accretion disks and clearly affects the properties of the related dynamo. This effect, however, may have been overestimated in previous work, and a careful study of the role played by boundaries will be required. [ABSTRACT FROM AUTHOR]

Aims. We use observations of solar activity to constrain parameters relating to the α effect in stochastic nonlinear dynamo models. Methods. This is achieved through performing a comprehensive statistical comparison by computing probability distribution functions (PDFs) of solar activity from observations and from our simulation of α - Ω mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11 000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain probability distribution functions (PDFs) of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α - Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α' parts. Results. By varying the correlation time τα of fluctuating α', the ratio of the amplitude of the fluctuating to mean alpha αR = √α'2≺/α20 (where angular brackets ≺ ≻ denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity when τα ϵ [22, 44] years with αR ϵ [0.21, 0.24]. [ABSTRACT FROM AUTHOR]

Context. Observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipoledominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance, which is quantified by the local Rossby number, is known to have a strong impact on the magnetic field geometry. Aims. We aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods. We have explored the similarities between anelastic dynamo models in spherical shells and observations of activeM-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we constructed observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results. The transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches. [ABSTRACT FROM AUTHOR]

The paper presents a study of a solar dynamo model operating in the bulk of the convection zone with the toroidal magnetic field flux concentrated in the subsurface rotational shear layer. We explore how this type of dynamo may depend on spatial variations of turbulent parameters and on the differential rotation near the surface. The mean-field dynamo model takes into account the evolution of magnetic helicity and describes its nonlinear feedback on the generation of large-scale magnetic field by the α-effect. We compare the magnetic cycle characteristics predicted by the model, including the cycle asymmetry (associated with the growth and decay times) and the duration--amplitude relation (Waldmeier's effects), with the observed sunspot cycle properties. We show that the model qualitatively reproduces the basic properties of the solar cycles. [ABSTRACT FROM AUTHOR]

It is shown that the saturated α-effect taken from the non-linear dynamo equations for the thin disc can still produce exponentially growing magnetic field in the case when this field does not feed back on the α. For negative dynamo number (stationary regime) stability is defined by the structure of the spectra of the linear problem for the positive dynamo numbers. The stability condition for the oscillatory solution (positive dynamo number) is also obtained and related to the phase shift of the original magnetic field, which produced saturated α and magnetic field in the kinematic regime. The results can be used to explain the similar effect observed in shell model simulations as well as in 3D dynamo models in the plane layer and sphere. [ABSTRACT FROM AUTHOR]

Abstract: The Solar Magnetic Field Telescope (SMFT) at the Huairou Solar Observing Station of the National Astronomical Observatory has been obtaining photospheric vector magnetograms on a daily basis for more than 20years. In this paper we first introduce our magnetograph and our data reduction routine. Then we focus on what we can learn from these vector magnetic field measurements about the magnetic non-potentiality of active regions. Derived physical quantities, such as shear angle, α value and current helicity, are good indicators of magnetic helicity. By studying values and evolutions of these physical quantities, we get a glimpse of the dynamo process in the solar interior. By examining the evolution of these quantities we can also learn what are the favorable conditions for coronal eruptions such as flares and coronal mass ejections. [Copyright &y& Elsevier]