Disk Dynamo Research Articles

Localized magnetorotational instability and its role in the accretion disc dynamo

(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 associated to MRI modes tends to reduce the magnetic energy, acting like a turbulent resistivity by mixing the non-uniform azimuthal field. Meanwhile, the azimuthal EMF generates a radial field that, in combination with the Keplerian shear, tends to amplify the azimuthal field and can therefore assist in the dynamo process. This effect, however, is reversed for sufficiently strong azimuthal fields, naturally leading to a saturation of the dynamo and possibly to a cyclic behaviour of the magnetic field, as found in previous numerical works.

A multi‐scale disk dynamo model

AbstractWe suggest to combine the mean‐field description of the galactic dynamo with a shell description of small‐scale turbulence for high values of hydrodynamic and magnetic Reynolds numbers. The model allows us to keep the balance of energy and realizes the kinematic and non‐linear regimes of the magnetic field generation. The suggested approach gives a possibility to study the role of magnetic helicity in the generation process. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Outflows and accretion in a star-disc system with stellar magnetosphere and disc dynamo

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 period of around 10 days. In the case of a stellar surface field strength of at least a few 100 G, the star is being spun up by the magnetic torque exerted on the star. The stellar accretion rates are always reduced by the presence of a magnetosphere which tends to divert a much larger fraction of the disc material into the wind. Both, a pressure-driven stellar wind and a disc wind form. In all our models with disc dynamo, the disc wind is structured and driven by magneto-centrifugal as well as pressure forces.

Non-local effects in the mean-field disc dynamo: II – numerical and asymptotic solutions

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 effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, , which is shown to persist in non-linear solutions where α-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre.

Ambient magnetic fields and dynamos: Pre-main sequence stars and elsewhere

The effects of an ambient (i.e. external) poloidal magnetic field on mean field dynamo action in a sphere are inves- tigated. It is found that an ambient field of strength comparable to that of the poloidal field of the isolated dynamo will inhibit dynamo action. This ambient field will normally be considerably weaker than the typical total field resulting from α 2 ω dynamo action. Given earlier similar results for disc dynamos, this appears to be a general result. Applications to pre-main sequence stars and the history of magnetic white dwarfs are discussed.

Accretion disc dynamos opened up by external magnetic fields

We show that a relatively weak poloidal external magnetic field, imposed in the outer parts of a Keplerian accretion disc, can open magnetic lines of a much stronger magnetic field generated by the dynamo in the inner disc. The resulting magnetic configuration can be favourable for launching a centrifugally driven wind. Even for a relatively weak external magnetic field (with energy density in excess of about only 10% of the thermal energy density at the outer disc radius) the geometry of the poloidal field in the disc neigbourhood is almost independent of the dynamo action, and is determined by the external field. The radial profile of the poloidal magnetic field on the disc surface is similar to that in the self-similar solution of Blandford & Payne (\cite{BP82}). We conclude that poloidal fields resulting from dynamo action can be important for launching a magneto-centrifugally driven outflow in accretion discs that occur in weakly magnetized environments, i.e. where an external field is too weak to be important. However, even a relatively weak external field can be wound up by the differential rotation to give a much stronger azimuthal field, and so modify dynamo action in the disc.

Automation specialists use machine vision as a system development tool

An automation solution for production testing of disk drives makes extensive use of machine vision - both as a system development tool and as integral part of the solution. Disk drive manufacturing is not a business for fainthearts, or slowcoaches. In less than two decades the number of drives shipped rose from 8 million to over 200 million; the price per megabyte of storage space fell from over $11 to less than $0.01; and transfer rates of 625 kilobytes/ second for your 1986 desktop drive seem strangely sad compared to the 320 megabytes/second on offer today. In a growth industry based on short product life cycles, manufacturers need exceptionally aggressive product development to survive. This means translating lab research into saleable product fast, while ensuring reliability, and it all adds up to fierce competition: 159 hard, floppy and optical disk drive manufacturers of fifteen years ago had slimmed down to just 68 by 2001. But there are opportunities for those who are innovative, well-equipped and brave enough to stake a development budget on delivering benefits to these hard pressed disk dynamos. Storage and network technology specialists Xyratex decided to invest in advanced automation.

Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al., A&A, v. 387, 453, 2002), to include also a quenching of turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the alpha effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the combined effect of algebraic and dynamic nonlinearities can limit the growth of the mean magnetic field. However, in contrast to our earlier work without quenching of the turbulent diffusivity, we cannot now find satisfactory solutions in the no-z approximation to the axisymmetric galactic dynamo problem.

Can a disc dynamo work in the laboratory?

Can a disc dynamo work in the laboratory?

Jet Collimation by Small‐Scale Magnetic Fields

A popular model for jet collimation is associated with the presence of a large-scale and predominantly toroidal magnetic field originating from the central engine (a star, a black hole, or an accretion disk). Besides the problem of how such a large-scale magnetic field is generated, in this model the jet suffers from the fatal long-wave mode kink magnetohydrodynamic instability. In this paper we explore an alternative model: jet collimation by small-scale magnetic fields. These magnetic fields are assumed to be local, chaotic, and tangled, but are dominated by toroidal components. Just as in the case of a large-scale toroidal magnetic field, we show that the "hoop stress" of the tangled toroidal magnetic fields exerts an inward force which confines and collimates the jet. The magnetic "hoop stress" is balanced either by the gas pressure of the jet or by centrifugal force if the jet is spinning. Since the length scale of the magnetic field is small (< the cross-sectional radius of the jet ≪ the length of the jet), in this model the jet does not suffer from the long-wave mode kink instability. Many other problems associated with the large-scale magnetic field are also eliminated or alleviated for small-scale magnetic fields. Though it remains an open question how to generate and maintain the required small-scale magnetic fields in a jet, the scenario of jet collimation by small-scale magnetic fields is favored by the current study on disk dynamo which indicates that small-scale magnetic fields are much easier to generate than large-scale magnetic fields.

SELF-EXCITING FARADAY DISK HOMOPOLAR DYNAMOS

In this paper we present an overview of recently published work on the Faraday disk self-exciting homopolar dynamos. We also extend the analysis of two such coupled self-exciting disk dynamos with linear series motors [Moroz et al., 1998a; Moroz et al., 1998b] to the situation where one or both dynamo subunits incorporate nonlinear motors. We examine the differences in some of the bifurcation transition sequences between the various cases and consider whether the nonlinear quenching of oscillatory solutions can occur [Hide, 1998].

Search for non-helical disc dynamos in simulations

The origin of large scale magnetic elds in accretion discs is investigated. Using global three-dimensional simulations of accretion disc turbulence, a recent suggestion of Vishniac & Cho (2001, ApJ 550, 752) is re-examined, according to which large scale elds in accretion discs could be understood without explicitly invoking the usual helicity eect. 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 typically also the cases where the resistivity is larger. The latter ones show signs typical of dynamo action based on the usual helicity eect. In the idealized simulations without rotation and just shear the above correlation is found to be particularly strong. In both cases there is, as expected, a systematic flux of magnetic helicity through the midplane. However, very little magnetic helicity leaves the domain through the top and bottom boundaries. The idealized simulations reveal that much of this systematic flux comes from the rotational component of the helicity flux and does not contribute to its divergence.

The effects of vertical outflows on disk dynamos

We consider the effect of vertical outflows on the mean-field dynamo in a thin disk. These outflows could be due to winds or magnetic buoyancy. We analyse both two-dimensional finite-difference numerical solutions of the axisymmetric dynamo equations and a free-decay mode expansion using the thin-disk approximation. Contrary to expectations, a vertical velocity can enhance dynamo action, provided the velocity is not too strong. In the nonlinear regime this can lead to super-exponential growth of the magnetic field. vide a study of the effects of vertical velocities. We show how vertical velocities can enhance the dynamo, allow- ing a larger growth rate and leading to super-exponential growth of the magnetic field in the nonlinear regime.

Stability criterion for projective synchronization in three-dimensional chaotic systems

Projective synchronization, in which the state vectors synchronize up to a scaling factor, has recently been observed in coupled partially linear chaotic systems (Lorenz system) under certain conditions. In this Letter, we present a stability criterion that guarantees the occurrence of the projective synchronization in three-dimensional systems. By applying the criterion to two typical partially linear systems (Lorenz and disk dynamo), it shows that only some parameters play the key role in influencing the stability. Projective synchronization only happens when σ>−1 for the Lorenz and μ>0 for the disk dynamo.

An unconventional accretion disc dynamo

In the light of recent results from numerical simulations of accretion disc MHD turbulence, we revisit the problem of the configuration of large-scale magnetic fields resulting from an αΩ dynamo operating in a thin accretion disc. In particular, we analyse the consequences of the peculiar sign of the α-effect suggested by numerical simulations. We determine the symmetry of the fastest-growing modes in the kinematic dynamo approximation and, in the framework of an ‘α-quenched’ dynamo model, study the evolution of the magnetic field. We find that the resulting field for this negative polarity of the α-effect generally has dipole symmetry with respect to the disc midplane, although the existence of an equilibrium configuration depends on the properties of the turbulence. The role of magnetic field dragging is discussed and, finally, the presence of an external uniform magnetic field is included to address the issue of magneto centrifugal wind launching from accretion discs.

Non-local effects in the mean-field disc dynamo I. An asymptotic expansion

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 weak (logarithmic) singularity. The integral term arises from non-local interactions of magnetic fields at different radii through vacuum outside the disc. The non-local interaction can have a stronger effect on the solution than the local radial diffusion in a thin disc, however the effect of the integral term is still qualitatively similar to magnetic diffusion.

The Role of the Likelihood Function in the Estimation of Chaos Models

The estimation problem for chaos models defined by deterministic differential equations is discussed, and the important role of the maximum likelihood method in the inferential study of chaos models is highlighted. The usefulness of the likelihood function in the inferential study of chaos is confirmed with numerical examples from the Lorenz chaos model and the Rikitake two disk dynamo chaos model.

The motion of magnetic fronts in spiral galaxies

We study the nonlinear asymptotic thin disc approximation to the mean field dynamo equations, as applicable to spiral galaxies. The circumstances in which sharp magnetic field structures (fronts) can propagate radially are investigated, and an expression for the speed of propagation derived. We find that the speed of an interior front is proportional to η//R * (where η is the diffusivity and Rt the galactic radius), whereas an exterior front moves with speed of order , where γ is the local growth rate of the dynamo. Numerical simulations are presented, that agree well with our asymptotic results. Further, we perform numerical experiments using the 'no-z' approximation for thin disc dynamos, and show that the propagation of magnetic fronts in this approximation can also be understood in terms of our asymptotic results.

Generic nonlinear processes in self–exciting dynamos and the long–term behaviour of the main geomagnetic field, including polarity superchrons

When the main geomagnetic field undergoes a reversal in polarity it does so in no more than a few thousand years. Many hundreds of such reversals must have occurred over geological time (the age of...

The structure of black hole magnetospheres -- I. Schwarzschild black holes

We introduce a multipolar scheme for describing the structure of stationary, axisymmetric, force-free black-hole magnetospheres in the ``3+1'' formalism. We focus here on Schwarzschild spacetime, giving a complete classification of the separable solutions of the stream equation. We show a transparent term-by-term analogy of our solutions with the familiar multipoles of flat-space electrodynamics. We discuss electrodynamic processes around disk-fed black holes in which our solutions find natural applications: (a) ``interior'' solutions in studies of the Blandford-Znajek process of extracting the hole's rotational energy, and of the formation of relativistic jets in active galactic nuclei and ``microquasars'', and, (b) ``exterior'' solutions in studies of accretion disk dynamos, disk-driven winds and jets. On the strength of existing numerical studies, we argue that the poloidal field structures found here are also expected to hold with good accuracy for rotating black holes, except for maximum possible rotation rates. We show that the closed-loop exterior solutions found here are not in contradiction with the Macdonald-Thorne theorem, since these solutions, which diverge logarithmically on the hole's horizon $\cal H$, apply only to those regions which exclude $\cal H$.