(abridged) MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result. Aims: We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action. Method: Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few orbits. The generation process of this field is investigated using the results of the simulations and an inhomogeneous linear approach. Results: The mechanism by which turbulence is sustained in zero-net-flux shearing boxes is shown to be related to the existence of a large-scale azimuthal field, surviving for several orbits. In particular, it is shown that MHD turbulence in shearing boxes can be seen as a dynamo process coupled to a magnetorotational-type instability.
We present numerical simulations of a self-sustaining magnetic field in a differentially rotating non-convective stellar interior. A weak initial field is wound up by the differential rotation; the resulting azimuthal field becomes unstable and produces a new meridional field component, which is then wound up anew, thus completing the `dynamo loop'. This effect is observed both with and without a stable stratification. A self-sustained field is actually obtained more easily in the presence of a stable stratification. The results confirm the analytical expectations of the role of Tayler instabi…
In low-mass Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars, anomalous mixing must transport material near the hydrogen-burning shell to the convective envelope. Recently, it was suggested that buoyant magnetic flux tubes could supply the necessary transport rate (Busso et al. 2007). The fields are assumed to originate from a dynamo operating in the stellar interior. Here, we show what is required of an $α-Ω$ dynamo in the envelope of an AGB star to maintain these fields. Differential rotation and rotation drain via turbulent dissipation and Poynting flux, so if shear can be res…
Supernovae are the dominant energy source for driving turbulence within the interstellar plasma. Until recently, their effects on magnetic field amplification in disk galaxies remained a matter of speculation. By means of self-consistent simulations of supernova-driven turbulence, we find an exponential amplification of the mean magnetic field on timescales of a few hundred million years. The robustness of the observed fast dynamo is checked at different magnetic Reynolds numbers, and we find sustained dynamo action at moderate Rm. This indicates that the mechanism might indeed be of relevance…
(Abriged) The magnetorotational instability (MRI) is believed to be an efficient way to transport angular momentum in accretion discs. It has also been suggested as a way to amplify magnetic fields in discs, the instability acting as a nonlinear dynamo. Recent numerical work has shown that a large-scale magnetic field, which is predominantly azimuthal, can be sustained by motions driven by the MRI of this same field. Following this idea, we present an analytical calculation of the MRI in the presence of an azimuthal field with a non-trivial vertical structure. We find that the mean radial EMF …
Are magnetic fields important in primordial star formation? Assuming that star formation occurs via an accretion disk that is turbulent, initially because of local gravitational instability, we calculate the disk structure for realistic accretion rates. We predict that local gravitational viscosity is able to drive accretion, without the disk fragmenting. We then estimate the rate of dynamo amplification of seed magnetic field. Turbulence in a stratified disk can be helical, with different signs of the helicity in each hemisphere. This provides a key ingredient for production of global scale m…
We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field. We focus on the non-axisymmetric instability that affects the toroidal magnetic field in a rotating star, which was first studied by Pitts and Tayler in the non-dissipative limit. According to Spruit, it could also drive a dynamo. The Pitts & Tayler instability is manifestly present in our simulations, with its conspicuous m=1 dependence in azimuth. But its analytic treatment used so far is too simplified to be applied to…
The kinematic evolution of axisymmetric magnetic fields in rotating magnetospheres of relativistic compact objects is analytically studied, based on relativistic Ohm's law in stationary axisymmetric geometry. By neglecting the poloidal flows of plasma in simplified magnetospheric models, we discuss self-excited dynamos due to the frame-dragging effect (originally pointed out by Khanna & Camenzind), and we propose alternative processes to generate axisymmetric magnetic fields against ohmic dissipation. The first process (which may be called induced excitation) is caused by the help of a backgro…
Core convection and dynamo activity deep within rotating A-type stars of 2 solar masses are studied with 3--D nonlinear simulations. Our modeling considers the inner 30% by radius of such stars, thus capturing within a spherical domain the convective core and a modest portion of the surrounding radiative envelope. The MHD equations are solved using the ASH code to examine turbulent flows and magnetic fields, both of which exhibit intricate time dependence. By introducing small seed magnetic fields into our progenitor hydrodynamic models rotating at one and four times the solar rate, we assess …
The operation of the solar global dynamo appears to involve many dynamical elements. Self-consistent MHD simulations which realistically incorporate all of these processes are not yet computationally feasible, though some elements can now be studied with reasonable fidelity. Here we consider the manner in which turbulent compressible convection within the bulk of the solar convection zone can generate large-scale magnetic fields through dynamo action. We accomplish this through a series of three-dimensional numerical simulations of MHD convection within rotating spherical shells using our ASH …
We explore the consequences of a magnetic dynamo origin for the viscosity in accretion discs, for the structure and evolution of discs in dwarf nova systems. We propose that the rapid cooling that sets in at the end of a dwarf nova eruption acts to inhibit the Balbus-Hawley instability, and thereby to quench dynamo action and so reduce disc viscosity. We demonstrate that a modified disc instability model can reproduce the basic properties of dwarf nova eruptions, as well as some properties of quiescent discs. We also discuss some observational consequences of our model.
We present an axisymmetric numerical model of a dynamo active accretion disc. If the dynamo-generated magnetic field in the disc is sufficiently strong (close to equipartition with thermal energy), a fast magneto-centrifugally driven outflow develops within a conical shell near the rotation axis, together with a slower pressure driven outflow from the outer parts of the disc as well as around the axis. Our results show that a dynamo active accretion disc can contribute to driving an outflow even without any external magnetic field. The fast outflow in the conical shell is confined by the azimu…
An axisymmetric model of a cool, dynamo-active accretion disc is applied to protostellar discs. Thermally and magnetically driven outflows develop that are not collimated within 0.1 AU. In the presence of a central magnetic field from the protostar, accretion onto the protostar is highly episodic, which is in agreement with earlier work.
The sunspot solar cycle has been usually explained as the result of a dynamo process operating in the sun. This is a classical problem in Astrophysics that until the present is not fully solved. Here we discuss current problems and limitations with the solar dynamo modeling and their possible solutions using a kinematic dynamo model within the Babcock-Leighton approximation as a tool. In particular, we discuss the importance of the turbulent magnetic pumping versus the meridional flow circulation in the dynamo operation.
A review of galactic magnetic fields is given with emphasis on simple analytical solutions of relevant equations and detailed comparison with observations. It is shown that mean-field dynamo theory, in its simplest form, is in a remarkably good agreement with observations of galactic magnetic fields. It is argued that the disc-halo connection can play crucial role in the nonlinear evolution of regular magnetic fields in spiral galaxies by driving flux of magnetic helicity from the disc, thus supporting healthy dynamo action.
It is argued that accretion discs in young stellar objects may have hot coronae that are heated by magnetic reconnection. This is a consequence of the magneto-rotational instability driving turbulence in the disc. Magnetic reconnection away from the midplane leads to heating of the corona which, in turn, contributes to driving disc winds.
The interaction between a protostellar magnetosphere and a surrounding dynamo-active accretion disc is investigated using an axisymmetric mean-field model. In all models investigated, the dynamo-generated magnetic field in the disc arranges itself such that in the corona, the field threading the disc is anti-aligned with the central dipole so that no X-point forms. When the magnetospheric field is strong enough (stellar surface field strength around 2 kG or larger), accretion happens in a recurrent fashion with periods of around 15 to 30 days, which is somewhat longer than the stellar rotation…
We examine the behaviour of an axisymmetric galactic dynamo model with a radial accretion flow in the disc. We also introduce a vertical magnetic flux through the galactic midplane, to simulate the presence of a large scale magnetic field trapped by the galaxy when forming. The trapped vertical flux is conserved and advected towards the disc centre by the radial flow. We confirm that accretion flows of magnitude several km/s through a significant part of the galactic disc can markedly inhibit dynamo action. Moreover, advection of the vertical flux in general results in mixed parity galactic fi…
The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of larg…
Magnetic helicity effects are discussed in laboratory and astrophysical settings. First, dynamo action in Taylor-Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Second, the build-up of a large scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils.…
The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, $Q(r)$ in the disc plane at a distance $r$ from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local …
Considerable progress has been made in understanding the hydrodynamics, but only to a certain extent the magnetohydrodynamics, of shaping bipolar outflows forming protoplanetary nebulae (PPNs) and planetary nebulae (PNs). In particular, Blackman et al. (2001b,2001a) point out two problems related to the formation of PNs and PPNs, regarding the formation of multipolar structures and the origin of the nebulae. They propose a solution by giving a semi-quantitative physical model which should be investigated by numerical simulations.
Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to…
The possibility of non-helical large scale dynamo action is investigated using three-dimensional simulations of global accretion discs as well as idealized local simulations without rotation and only shear. Particular emphasis is placed on a certain correlation between vorticity and azimuthal velocity gradient which has been predicted to drive large scale dynamo action, independent of the presence or absence of kinetic helicity. In the global disc simulations two types of behaviours are found: those which do show this type of velocity correlation and those which do not. The former ones are typ…
Two examples of magnetic anti-dynamos in magnetohydrodynamics (MHD) are given. The first is a 3D metric conformally related to Arnold cat fast dynamo metric: ${ds_{A}}^{2}=e^{-λz}dp^{2}+e^{λz}dq^{2}+dz^{2}$ is shown to present a behaviour of non-dynamos where the magnetic field exponentially decay in time. The curvature decay as z-coordinates increases without bounds. Some of the Riemann curvature components such as $R_{pzpz}$ also undergoes dissipation while component $R_{qzqz}$ increases without bounds. The remaining curvature component $R_{pqpq}$ is constant on the torus surface. The other …
We reconsider thin-disc global asymptotics for kinematic, axisymmetric mean-field dynamos with vacuum boundary conditions. Non-local terms arising from a small but finite radial field component at the disc surface are consistently taken into account for quadrupole modes. As in earlier approaches, the solution splits into a local part describing the field distribution along the vertical direction and a radial part describing the radial (global) variation of the eigenfunction. However, the radial part of the eigenfunction is now governed by an integro-differential equation whose kernel has a wea…
Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.
For a simple spherically symmetric mean-field dynamo model we investigate the possibility of determining the radial dependence of the coefficient $α$. Growth rates for different magnetic field modes are assumed to be known by measurement. An evolutionary strategy (ES) is used for the solution of the inverse problem. Numerically, we find quite different $α$-profiles giving nearly the same eigenvalues. The ES is also applied to find functions $α(r)$ yielding zero growth rates for the lowest four magnetic field modes. Additionally, a slight modification of the ES is utilized for an ''energetic'' …
Recent experiments have shown that it is possible to study a fundamental astrophysical process such as dynamo action in controlled laboratory conditions using simple MHD flows. In this paper we explore the possibility that Taylor-Couette flow, already proposed as a model of the magneto-rotational instability of accretion discs, can sustain generation of magnetic field. Firstly, by solving the kinematic dynamo problem, we identify the region of parameter space where the magnetic field's growth rate is higher. Secondly, by solving simultaneously the coupled nonlinear equations which govern veloc…
A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between the alpha-effect and the inverse cascade of magnetic helicity is highlighted. The possibility of `catastrophic' quenching of the alpha-effect is explained in terms of the constraint placed by the conservation of magnetic helicity.
Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a …
We present a new fast dynamo model for galactic magnetic fields, which is based on the Parker-shearing instability and magnetic reconnection, in the spirit of the model proposed by Parker (1992). We introduce a new scenario of flux tube interactions and estimate the dynamo transport coefficient basing on simple geometrical arguments. The obtained expressions are equivalent to the formally derived helicity $α_d$ and diffusivity $η_d$ in the first paper of this series. The model we propose predicts that the $α$-effect in galactic discs has opposite sign with respect to that resulting directly fr…
Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than res…
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no the back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of the kinematic dynamo theory to protogalaxies is rather limited. The reason is th…
Mean field dynamo theory is a leading candidate to explain the observed large scale magnetic fields of galaxies and stars. However, controversy arises over the extent of premature quenching by the backreaction of the growing field. We distinguish between rapid mean field dynamo action, which is required by astrophysical systems, and resistively limited action. We show how the flow of magnetic helicity is important for rapid action. Existing numerical and analytic work suggesting that mean field dynamos are prematurely quenched and resistively limited include approximations or boundary conditio…
We study the changes in the dynamical behaviour of axisymmetric spherical mean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full sphere to spherical shell, torus and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models considered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, the most easily excited fields are oscillatory, in one case with dipolar symm…
The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic f…
It is shown that the turbulent dynamo $α$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is electrostatic or due to the electron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity except for resistive effects and a small battery effect. Implications for astrophysical situations, especially for the solar dynamo, are discussed.
The possibility of fast dynamo action by collisionless kinetic Alfven Wave turbulence is demonstrated. The irreversibility necessary to lock in the generated field is provided by electron Landau damping, so the induced electric field does not vanish with resistivity. Mechanisms for self-regulation of the system and the relation of these results to the theory of alpha quenching are discussed. The dynamo-generated fields have symmetry like to that of zonal flows, and thus are termed zonal fields.
After the dynamo experiment in November 1999 had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.
