Non-linear magnetic diffusivity in mean-field electrodynamics

We consider non-linear transport and drift processes caused by an inhomogeneous magnetic field in a turbulent fluid. The coefficients of magnetic diffusivity and drift velocity are calculated by making use of the second-order correlation approximation. Transport processes in the presence of a sufficiently strong magnetic field become anisotropic with larger diffusion rate and turbulent electrical resistivity across the field than along the field. Non-linear effects also lead to a drift of the magnetic field away from the regions with a higher magnetic energy.     

Magnetic and optical spiral arms in the galaxy NGC 6946

The spiral pattern in the nearby spiral galaxy NGC 6946 has been studied using the wavelet transformation technique, applied to galaxy images in polarized and total non-thermal radio emission at λλ 3.5 and 6.2 cm, in broadband red light, in the λ 21.1 cm H  i line and in the optical Hα line. Well-defined, continuous spiral arms are visible in polarized radio emission and red light, where we can isolate a multi-armed pattern in the range of galactocentric distances 1.5–12 kpc, consisting of four long arms and one short spiral segment. The 'magnetic arms' (visible in polarized radio emission) are localized almost precisely between the optical arms. Each magnetic arm is similar in length and pitch angle to the preceding optical arm (in the sense of galactic rotation) and can be regarded as its phase-shifted image. Even details like a bifurcation of an optical arm have their phase-shifted counterparts in the magnetic arms. The average relative amplitude of the optical spiral arms (the stellar density excess over the azimuthal average) grows with galactocentric radius up to 0.3–0.7 at r ≃5 kpc, decreases by a factor of two at r =5–6 kpc and remains low at 0.2–0.3 in the outer parts of the galaxy. By contrast, the magnetic arms have a constant average relative amplitude (the excess in the regular magnetic field strength over the azimuthal average) of 0.3–0.6 in a wide radial range r =1.5–12 kpc. We briefly discuss implications of our findings for theories of galactic magnetic fields.     

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)     

3D global simulations of galactic magnetic fields and gas flows

The evolution of three-dimensional (3D), dynamo excited galactic magnetic fields under the influence of a time-dependent gas flow in spiral arms is already well investigated. Our principal goal is to check how the dynamo-driven turbulent magnetic fields affect the gas flows. Numerical solutions of the full set of 3D MHD equations for dynamos in spiral galaxies are presented. Further we try to investigate the nonlinear evolution of magnetic instabilities in a global galactic model. The model includes differential rotation, eddy diffusivity and tensorial alpha-effect. In a first step the flow is driven by a prescribed gravitational potential. The vertical density stratification and the radial-azimutal spiral pattern are taken closely to observational data. We use a modified variant of the highly parallelized time-stepping ZeusMP code for the simulations of global galactic magnetic fields and gas flows. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the validity of quasi-linear kinematic mean-field electrodynamics in astrophysical flows

Mean-field theory in its kinematic form with the quasi-linear approximation is widely used for the modelling of the transport of weak magnetic fields in turbulent media. The validity of this approach to real astrophysical flows is discussed. Numerically evaluating the turbulent electromotive force using Lagrangian analysis for a set of simple, prescribed 2D flow patterns with a wide range of parameters, we find that quasi-linear expressions for the turbulent diffusivities and for the pumping velocities are correct within a factor of 2 for a wide variety of flow types with order of unity (or even higher) effective Strouhal numbers. The degree of the non-linear quenching of turbulent transport by a weak magnetic field is also discussed. We argue that, owing to the intermittency and small filling factors of magnetic fields in realistic astrophysical media, diffusivity and pumping effects are not quenched to order of magnitude, while a more moderate quenching of order 10 per cent is still present.     

3D numerical models of magnetic field evolution in galaxies interacting with the ICM

A fully three-dimensional (3D) MHD model is applied to simulate the evolution of large-scale magnetic field in galaxies interacting with the intra-cluster medium (ICM). As the model input we use a time dependent velocity field of gas clouds (HI) resulting from 3D N-body sticky-particle model of a galaxy. These clouds are affected by ram pressure due to their rapid motion through the ICM. The gas evolves in an analytically given gravitational potential which includes a dark matter halo, a disk, and a bulge component. We found that due to the interaction with the ICM the resultant magnetic field correctly reproduces the observed structures of the magnetic field forming peculiar spiral arms and magnetic features widely observed in cluster spiral galaxies. This revised version was published online in September 2006 with corrections to the Cover Date.     

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)     

Magnetic fields and the dynamics of spiral galaxies

We investigate the dynamics of magnetic fields in spiral galaxies by performing 3D magnetohydrodynamics simulations of galactic discs subject to a spiral potential using cold gas, warm gas and a two-phase mixture of both. Recent hydrodynamic simulations have demonstrated the formation of interarm spurs as well as spiral arm molecular clouds, provided the interstellar medium model includes a cold H  i phase. We find that the main effect of adding a magnetic field to these calculations is to inhibit the formation of structure in the disc. However, provided a cold phase is included, spurs and spiral arm clumps are still present if β≳ 0.1 in the cold gas. A caveat to the two-phase calculations though is that by assuming a uniform initial distribution, β≳ 10 in the warm gas, emphasizing that models with more consistent initial conditions and thermodynamics are required. Our simulations with only warm gas do not show such structure, irrespective of the magnetic field strength.
Furthermore, we find that the introduction of a cold H  i phase naturally produces the observed degree of disorder in the magnetic field, which is again absent from simulations using only warm gas. Whilst the global magnetic field follows the large-scale gas flow, the magnetic field also contains a substantial random component that is produced by the velocity dispersion induced in the cold gas during the passage through a spiral shock. Without any cold gas, the magnetic field in the warm phase remains relatively well ordered apart from becoming compressed in the spiral shocks. Our results provide a natural explanation for the observed high proportions of disordered magnetic field in spiral galaxies and we thus predict that the relative strengths of the random and ordered components of the magnetic field observed in spiral galaxies will depend on the dynamics of spiral shocks.     

Milestones in the Observations of Cosmic Magnetic Fields

Magnetic fields are observed everywhere in the universe. In this review, we concentrate on the observational aspects of the magnetic fields of Galactic and extragalactic objects. Readers can follow the milestones in the observations of cosmic magnetic fields obtained from the most important tracers of magnetic fields, namely, the star-light polarization, the Zeeman effect, the rotation measures (RMs, hereafter) of extragalactic radio sources, the pulsar RMs, radio polarization observations, as well as the newly implemented sub-mm and mm polarization capabilities. The magnetic field of the Galaxy was first discovered in 1949 by optical polarization observations. The local magnetic fields within one or two kpc have been well delineated by starlight polarization data. The polarization observations of diffuse Galactic radio background emission in 1962 confirmed unequivocally the existence of a Galactic magnetic field. The bulk of the present information about the magnetic fields in the Galaxy comes from anal     

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.     

Hydrostatic equilibrium in a magnetized, warped Galactic disc

Hydrostatic equilibrium of the multiphase interstellar medium in the solar vicinity is reconsidered, with the regular and turbulent magnetic fields treated separately. The regular magnetic field strength required to support the gas is consistent with independent estimates, provided that energy equipartition is maintained between turbulence and random magnetic fields. Our results indicate that a mid-plane value of B ₀=4 μG for the regular magnetic field near the Sun leads to more attractive models than B ₀=2 μG . The vertical profiles of both the regular and random magnetic fields contain disc and halo components, the parameters of which we have determined. The layer at 1≲| z |≲4 kpc can be overpressured and an outflow at a speed of about 50 km s⁻¹ may occur there, presumably associated with a Galactic fountain flow, if B ₀≃2 μG .
We show that hydrostatic equilibrium in a warped disc must produce asymmetric density distributions in z , in rough agreement with H  i observations in the outer Galaxy. This asymmetry may be a useful diagnostic of the details of the warping mechanism in the Milky Way and other galaxies. We find indications that gas and magnetic field pressures are different above and below the warped midplane in the outer Galaxy, and quantify the difference in terms of turbulent velocity and/or magnetic field strength.     

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

Gas motions in the plane of the spiral galaxy NGC 3631

The velocity field of the nearly face-on galaxy NGC 3631, derived from observations in the H α line and H  i radio line, is analysed to study perturbations related to the spiral structure of the galaxy. We confirm our previous conclusion that the line-of-sight velocity field gives evidence of the wave nature of the observed two-armed spiral structure. Fourier analysis of the observed velocity field is used to determine the location of corotation of the spiral structure of this galaxy, and the radius of corotation R _c is found to be about 42 arcsec, or 3.2 kpc. The vector velocity field of the gas in the plane of the disc is restored, and, taking into account that we previously investigated vertical motions, we now have a full three-dimensional gaseous velocity field of the galaxy. We show clear evidence of the existence of two anticyclonic and four cyclonic vortices near corotation in a frame of reference rotating with the spiral pattern. The centres of the anticyclones lie between the observed spiral arms. The cyclones lie close to the observed spirals, but their centres are shifted from the maxima in brightness.     

Magnetic field evolution in simulations with Euler potentials

Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation.     

Spurs and feathering in spiral galaxies

We present smoothed particle hydrodynamic (SPH) simulations of the response of gas discs to a spiral potential. These simulations show that the commonly observed spurs and feathering in spiral galaxies can be understood as being due to structures present in the spiral arms that are sheared by the divergent orbits in a spiral potential. Thus, dense molecular cloud-like structures generate the perpendicular spurs as they leave the spiral arms. Subsequent feathering occurs as spurs are further sheared into weaker parallel structures as they approach the next spiral passage. Self-gravity of the gas is not included in these simulations, stressing that these features are purely due to the hydrodynamics in spiral shocks. Instead, a necessary condition for this mechanism to work is that the gas need be relatively cold (1000 K or less) in order that the shock is sufficient to generate structure in the spiral arms, and such structure is not subsequently smoothed by the gas pressure.     

Magnetic fields and radio polarization of barred galaxies

In order to simulate evolution of a large-scale magnetic field in a barred galaxy possessing a gaseous halo we apply a three-dimensional (3D) MHD numerical model. We solve a induction equation using a time-dependent velocity field of molecular gas resulting from self-consistent 3D N-body simulations of a galactic disk. The gaseous halo rotates differentially co-rotating with the disk. In our model we introduce the dynamo process causing the amplification of the magnetic field as well as the formation of field structures high above the galactic disk. The simulated magnetic fields are used to construct the models of a high-frequency (Faraday rotation-free) polarized radio emission that accounts for effects of projection and limited resolution, and is thus suitable for direct comparison with observations. We found that the resultant magnetic field correctly reproduces the observed structures of polarization B-vectors, forming coherent patterns well aligned with spiral arms and with the bar. The process initializing a wave-like behavior of the magnetic field, which efficiently forms magnetic maxima between the spiral arms, is demonstrated. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the meaning and inapplicability of the Zeldovich relations of magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two‐dimensions, followed by others for three dimensions, have presented formulae of the form 〈b²〉 = f(R_M) . Such “Zeldovich relations” have sometimes been interpreted to provide steady‐state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function f that depends on spatial dimension and a magnetic Reynolds number R_M. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. In 3D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of R_M and the initially imposed , as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re‐analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady‐states of large R_M MHD turbulence. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

Diamagnetic pumping near the base of a stellar convection zone

The property of inhomogeneous turbulence in conducting fluids to expel large‐scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity η_T of the convection zone to the (microscopic or turbulent) diffusivity η_in of the radiative interior is η_T/η_in ≥ 10⁵. Confinement in younger stars requires larger η_T/η_in. The observation of persistent magnetic structures on young solar‐type stars can thus provide evidence for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)