Magnetic flux expulsion in powerful superbubble explosions and the α–Ω dynamo

The possibility of magnetic flux expulsion from the Galaxy in superbubble (SB) explosions, important for the α –Ω dynamo, is considered. Special emphasis is put on investigation of the downsliding of the matter from the top of the shell formed by the SB explosion, which is able to influence the kinematics of the shell. It is shown that either Galactic gravity or the development of the Rayleigh–Taylor instabilities in the shell limit the SB expansion, thus making magnetic flux expulsion impossible. The effect of cosmic rays in the shell on the sliding is considered, and it is shown that it is negligible compared with Galactic gravity. Thus the question of the possible mechanism of flux expulsion in the α –Ω dynamo remains open.     

An accretion disc model with a magnetic wind and turbulent viscosity

A model is presented for an accretion disc with turbulent viscosity and a magnetically influenced wind. The magnetic field is generated by a dynamo in the disc, involving the turbulence and radial shear. Disc-wind solutions are found for which the wind mass flux is sufficient to play a major part in driving an imposed steady inflow, but small enough for most material to be accreted on to the central object. Constraints arise for the magnetic Reynolds and Prandtl numbers in terms of the turbulent Mach number and vertical length-scale of the disc's horizontal magnetic field. It is shown that the imposition of a stellar boundary condition enhances the wind mass flux in the very inner region of the disc and may result in jet formation.     

Dynamo saturation in direct simulations of the multi‐phase turbulent interstellar medium

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean‐field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical‐flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean‐field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three‐dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing‐periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean‐field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched α) dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub‐grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fast galactic dynamos and interstellar magnetic bubbles

Large ( > 100 pc) interstellar magnetic bubbles are necessary in the cosmic-ray-driven fast galactic dynamo, as pioneered by Parker in 1992. In a first part, a look is made at the available data on nearby (< 1000 pc) large interstellar magnetic bubbles. Here the magnetic field strengthB in a large shell of densityn around an OB association is found to be a few times greater than that outside in the general interstellar medium, varying typically likeB ~n, as expected for a shocked medium. In a second part, some tests are made of the predictions about interstellar magnetic bubbles made by the theory of a cosmic-ray driven fast galactic dynamo. The bubble tests generally support the idea of a cosmic-ray-driven fast galactic dynamo for the Milky Way.     

Comparisons and connections between mean field dynamo theory and accretion disc theory

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)     

Dynamo Dominated Accretion and Energy Flow: The Mechanism of Active Galactic Nuclei

An explanation of the magnetic fields of the universe, the central mass concentration of galaxies, the massive black hole of every galaxy, and the AGN phenomena has been an elusive goal. We suggest here the outlines of such a theoretical understanding and point out where the physical understanding is missing. We believe there is an imperative to the sequence of mass flow and hence energy flow in the collapse of a galactic mass starting from the first non-linearity appearing in structure formation following decoupling. This first non-linearity of a two to one density fluctuation, the Lyman-α clouds, ultimately leads to the emission spectra of the phenomenon of AGN, quasars, blazars etc. The over-arching physical principle is the various mechanisms for the transport of angular momentum. We believe we have now understood the new physics of two of these mechanisms that have previously been illusive and as a consequence they impose strong constraints on the initial conditions of the mechanisms for the subsequent emission of the gravitational binding energy. The new phenomena described here are: 1) the Rossby vortex mechanism of the accretion disk viscosity, and 2) the mechanism of the α - Ω dynamo in the accretion disk. The Rossby vortex mechanism leads to a prediction of the black hole mass and rate of energy release and the α - Ω dynamo leads to the generation of the magnetic flux of the galaxy (and the far greater magnetic flux of clusters) and separately explains the primary flux of energy emission as force-free magnetic energy density. This magnetic flux and magnetic energy density separately are the necessary consequence of the saturation of a dynamo created by the accretion disk with a gain greater than unity. The predicted form of the emission of both the flux and the magnetic energy density is a force-free magnetic helix extending axially from the disk a distance depending upon its winding number and radius of its flux surfaces, a distance of Mpc's. This Poynting flux of magnetic energy would be invisible unless the currents bounding the magnetic field are dissipated. By definition of force-free, these currents are parallel to the field and throughout its volume. Therefore the dissipation must be throughout the volume as opposed to the conventional reconnection which takes place only at surface layers. This radically different interpretation of reconnection is supported by the observation of "interruption" events in fusion tokamak experiments. Here, and presumably in the galactic case as well, the parallel currents and their dissipation is mediated by run-away, high energy electrons and ions. It is then natural to seek an explanation for the emission spectrum of the dynamo-produced Poynting flux in the same synchrotron emission associated with the dissipation of these run-away currents. We propose the radically different view that these ultra high energy, run-away electrons directly produce the emission spectra as compared to the published models that assume an acceleration of bulk matter to a γ ∼ 10 and then reconvert this kinetic energy by shock heating into a highly relativistic plasma, γ ∼ 10⁶. This revised version was published online in July 2006 with corrections to the Cover Date.     

Can turbulent plane‐shear flows support large‐scale dynamos?

Turbulent plane‐shear flow is found to show same basic effects of mean‐fieldMHD as rotating turbulence. In particular, the mean electromotive force (EMF) includes highly anisotropic turbulent diffusion and alpha‐effect. Only magnetic diffusion remains for spatially‐uniform turbulence. The question is addressed whether in this case a self‐excitation of a magnetic field by so‐called sher‐current dynamo is possible and the quasilinear theory provides a negative answer. The streamaligned component of the EMF has the sign opposite to that required for dynamo. If, however, the turbulence is not uniform across the flow direction then a dynamo‐active α ‐effect emerges. The critical magnetic Reynolds number for the alpha‐shear dynamo is estimated to be slightly above ten. Possibilities for cross‐checking theoretical predictions with MHD experiments are discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the parametric resonance in a thin disk galactic dynamo

The absence of a parametric resonance by the generation of a large scale bisymmetric magnetic field in a thin galactic disk with periodically time dependent properties in the frames of the simplest thin disk galactic dynamo model is shown.     

Modeling the total and polarized emission in evolving galaxies: “Spotty” magnetic structures

Future radio observations with the Square Kilometre Array (SKA) and its precursors will be sensitive to trace spiral galaxies and their magnetic field configurations up to redshift z ≈ 3. We suggest an evolutionary model for the magnetic configuration in star‐forming disk galaxies and simulate the magnetic field distribution, the total and polarized synchrotron emission, and the Faraday rotation measures for disk galaxies at z ≲ 3. Since details of dynamo action in young galaxies are quite uncertain, we model the dynamo action heuristically relying only on well‐established ideas of the form and evolution of magnetic fields produced by the mean‐field dynamo in a thin disk. We assume a small‐scale seed field which is then amplified by the small‐scale turbulent dynamo up to energy equipartition with kinetic energy of turbulence. The large‐scale galactic dynamo starts from seed fields of 100 pc and an averaged regular field strength of 0.02 μG, which then evolves to a “spotty” magnetic field configuration in about 0.8 Gyr with scales of about one kpc and an averaged regular field strength of 0.6 μG. The evolution of these magnetic spots is simulated under the influence of star formation, dynamo action, stretching by differential rotation of the disk, and turbulent diffusion. The evolution of the regular magnetic field in a disk of a spiral galaxy, as well as the expected total intensity, linear polarization and Faraday rotation are simulated in the rest frame of a galaxy at 5GHz and 150 MHz and in the rest frame of the observer at 150 MHz. We present the corresponding maps for several epochs after disk formation. Dynamo theory predicts the generation of large‐scale coherent field patterns (“modes”). The timescale of this process is comparable to that of the galaxy age. Many galaxies are expected not to host fully coherent fields at the present epoch, especially those which suffered from major mergers or interactions with other galaxies. A comparison of our predictions with existing observations of spiral galaxies is given and discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Implications of mean field accretion disc theory for vorticity and magnetic field growth

In addition to the scalar Shakura–Sunyaev α _ss turbulent viscosity transport term used in simple analytic accretion disc modelling, a pseudo-scalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and each hemisphere is separately studied. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudo-scalar terms have been studied, and can lead to large-scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent with those required for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former pseudo‐scalar can more easily reverse sign in the two cases.     

Reconnection X-winds: spin-down of low-mass protostars

We investigate the interaction of a protostellar magnetosphere with a large-scale magnetic field threading the surrounding accretion disc. It is assumed that a stellar dynamo generates a dipolar-type field with its magnetic moment aligned with the disc magnetic field. This leads to a magnetic neutral line at the disc mid-plane and gives rise to magnetic reconnection, converting closed protostellar magnetic flux into open field lines. These are simultaneously loaded with disc material, which is then ejected in a powerful wind. This process efficiently brakes down the protostar to 10–20 per cent of the break-up velocity during the embedded phase.     

Spot signatures of a solar‐type dynamo in close binary stars

Magnetic activity signatures in the atmosphere of active stars can be used to place constrains on the underlying processes of flux transport and dynamo operation in its convective envelope. The ‘solar paradigm’ for magnetic activity suggests that the magnetic field is amplified and stored at the base of the convection zone. Once a critical field strength is exceeded, perturbations initiate the onset of instabilities and the growth of magnetic flux loops, which rise through the convection zone, emerge at the stellar surface, and eventually lead to the formation of starspots and active regions. In close binaries, the proximity of the companion star breaks the rotational symmetry. Although the magnitude of tidal distortions is rather small, non‐linear MHD simulations have nevertheless shown in the case of main‐sequence binary components that they can cause non‐uniform surface distributions of flux tube eruptions. The present work extends the investigation to post‐mainsequence components to explore the specific influence of the stellar structure on the surface pattern of erupting flux tubes. In contrast to the case of main‐sequence components, where the consistency between simulation results and observations supports the presumption of a solar‐like dynamo mechanism, the numerical results here do not recover the starspot properties frequently observed on evolved binary components. This aspect points out an insufficiency of the applied flux tube model and leads to the conclusion that additional flux transport and possibly amplification mechanisms have to be taken into account. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can the turbulent galactic dynamo generate large-scale magnetic fields?

Large-scale magnetic fields in galaxies are thought to be generated by a turbulent dynamo. However, the same turbulence also leads to a small-scale dynamo which generates magnetic noise at a more rapid rate. The efficiency of the large-scale dynamo depends on how this noise saturates. We examine this issue, taking into account ambipolar drift, which obtains in a galaxy with significant neutral gas. We argue as follows.
(i) The small-scale dynamo generated field does not fill the volume, but is concentrated into intermittent rope-like structures. The flux ropes are curved on the turbulent eddy scales. Their thickness is set by the diffusive scale determined by the effective ambipolar diffusion.
(ii) For a largely neutral galactic gas, the small-scale dynamo saturates, as a result of inefficient random stretching, when the peak field in a flux rope has grown to a few times the equipartition value.
(iii) The average energy density in the saturated small-scale field is subequipartition, since it does not fill the volume.
(iv) Such fields neither drain significant energy from the turbulence nor convert eddy motion of the turbulence on the outer scale into wave-like motion. The diffusive effects needed for the large-scale dynamo operation are then preserved until the large-scale field itself grows to near equipartition levels.     

Dynamo theories of the solar and galactic magnetic fields

Earlier criticisms of solar and galactic dynamo theories are extended to answer Parker's rebuttal, and the major modification made to his models to include Sweet's magnetic field annihilation mechanism as invoked in some theories of solar flares. His kinematic and weak-field analyses appear irrelevant because they ignore magnetic stresses which are of major importance and whose effects are evident in sunspots and elsewhere. It is shown that, even if Sweet's mechanism is effective under the most favourable conditions, these conditions are most unlikely in the solar convection zone or galactic disk.The problem is resolved by observational data which show that the fields are not tangled down to the scales required for dissipation byany known mechanism in the times available. Spot groups and many other patterns show that the solar fields are much too ordered to be products of a region of turbulence or to be dissipated by turbulence; the toroidal field must leave the Sun entirely to complete each 11-yr cycle. Faraday rotation, H I gas observations and extra-galactic fields provide strong evidence against a galactic dynamo and for a primordial field.     

Global structure of self-excited magnetic fields arising from the magnetic shear instability

The global structure of a self-excited magnetic field arising from the magnetic shear instability has been simulated in spherical geometry by a 3D fully non-linear approach. In order to model the structure of an accretion disc we prescribe a rotation profile of the Brandt type which is Keplerian in the outer regions but yields rigid rotation at the inner core. We performed a whole series of runs at different dynamo numbers with an increasing number of modes in spectral space, thereby checking the influence of the numerical resolution in our simulations. Starting from arbitrary small perturbations, the magnetic and kinetic energies grow by several orders of magnitude as soon as a certain azimuthal resolution of at least m =15 was used at a dynamo number of order C =10⁵. Several phases of the transition to turbulence are realized and interpretations are given for the respective effects occurring at each stage. The resulting magnetic field is highly non-axisymmetric and possesses a pronounced inhomogeneous vortex structure of twisted flux tubes. The flow is almost axisymmetric but shows a Kolmogorov-like behaviour for small scales. The outer surface of the shell is penetrated by magnetic field lines in spot-like regions, which are located mainly in the equatorial plane. For very high dynamo numbers we find a cyclic behaviour of the averaged magnetic field amplitude. The problem of angular momentum transport is discussed in terms of the ShakuraSunyaev viscosity alpha , which depends exponentially on the radial distance and adopts values in the range 10³10⁵.     

Non‐holonomic filamentary dynamos as generalized Arnold's maps in Riemannian space

A filamentary non‐holonomic dynamo solution of self‐induction magnetic field equation is found by considering highly conducting filaments. It is shown that planar filaments cannot support dynamo action since the flow along the filament vanishes for torsion‐free filaments. This is a generalization of the Zeldovich theorem for linear magnetic dynamo filaments. The flow of filament is proportionally to the product between Frenet torsion and curvature. This shows that filamentary dynamos must possess Frenet torsion. A well‐known example of this result is the α ‐dynamo in solar physics. Magnetic helicity and magnetic energy for this filamentary dynamo are computed. Magnetic helicity vanishes by construction and the magnetic field decays with torsion energy in helicoidal dynamos. The approach considered here is useful for the investigation of anisotropic turbulent cascades. As a particular simple example it is shown that under certain constraints the solution can be reduced to the Arnold cat dynamo map solution where the non‐holonomic directional mixed derivative, would play the role of the Lyapunov exponent which appears on stretching the magnetic field in Riemannian space. The solution seems to describe marginal slow dynamos when the velocities involved in the dynamo flows are constants. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stellar dynamo driven wind braking versus disc coupling

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 a perfect stellar dipole field, dynamo‐generated stellar fields favor field‐aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 α Ω 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.     

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

The kinematic dynamo equations for the mean magnetic field are solved with an asymptotic method of the WKB type. The excitation conditions and main characteristics of the non-axially symmetric modes for a given distribution of the sources are obtained. Utilization of the helioseismologic data on the Sun's internal rotation permits an explanation, within the framework of dynamo theory, of the excitation of the main non-axially symmetric modes revealed in the Sun's magnetic field sector structure.     

The effect of the neutron-star crust on the evolution of a core magnetic field

We consider the expulsion of the magnetic field from the super-conducting core of a neutron star and its subsequent decay in the crust. Particular attention is paid to a strong feedback of the distortion of magnetic field lines in the crust on the expulsion of the flux from the core. This causes a considerable delay in the core flux expulsion if the initial field strength is larger than 10¹¹ G. It is shown that the hypothesis on the magnetic field expulsion induced by the neutron-star spin-down is adequate only for a relatively weak initial magnetic field B ≈10¹¹ G. The expulsion time-scale depends not only on the conductivity of the crust, but also on the initial magnetic field strength itself. Our model of the field evolution naturally explains the existence of the residual magnetic field of neutron stars. Its strength is correlated with the impurity concentration in neutron-star crusts and anticorrelated with the initial field strengths.