The generation and dissipation of solar and galactic magnetic fields

Turbulent diffusion of magnetic field plays an essential role in the generation of magnetic field in most astrophysical bodies. This paper reviews what can be proved, and what can be believed, about the turbulent diffusion of magnetic field. Observations indicate the dissipation of magnetic field at rates that can be understood only in terms of turbulent diffusion. Theory shows that a largescale weak magnetic field diffuses in a turbulent flow in the same way that smoke is mixed throughout the fluid by the turbulence. The small-scale fields (produced from the large-scale field by the turbulence) are limited in their growth by reconnection of field lines at neutral points, so that the turbulent mixing of field and fluid is not halted by them.Altogether, it appears that the mixing of field and fluid in the observed turbulent motions in the Sun and in the Galaxy is unavoidable. Turbulent diffusion causes decay of the general solar fields in a decade or so, and of the galactic field in 10⁸–10⁹ yr. We conclude that continual dynamo action is implied by the observed existence of the fields.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.     

Spectrum of the galactic magnetic fields

The magnetic fields observed in the galactic disc are generated by the differential rotation and the helical turbulent motions of interstellar gas. On the scalesl=2k ^–1 which lie in the intervall ₀<l<l _e (l ₀100 pc is the energy-range scale of the galactic turbulence), the spectral density of the kinetic energy of turbulence (k ^–5/3) exceeds the magnetic energy spectral density (k ^–1). The equipartition between magnetic and kinetic energies is reached atl=l _e 6 pc in the intercloud medium and is maintained down to the scalel=l _d 0.03 pc. In dense interstellar cloudsl _e is determined by the individual cloud size andl _d 0.1 pc.The internal turbulent velocities in Hi clouds (cloud size is assumed to be 10 pc) lie in the range from 1.8 to 5.6km s^–1, fitting well within the observed range of internal rms velocities. Dissipation of the interstellar MHD turbulence leads to creation of temperature fluctuations with amplitudes of 150 K and 65 K in dense clouds and intercloud medium, respectively. The small-scale fluctuations observed in the interstellar medium may arise from such perturbations due to the thermal instability, for instance. Dissipation of the MHD turbulence energy provides nearly half of the energy supply needed to maintain the thermal balance of the interstellar medium.     

On the origin of galactic magnetic fields

We discuss the properties of the large-scale galactic magnetic fields which can help to discriminate between theories of their origin. We argue that the mean-field dynamo theory in its simplest form is unique in that it can explain most of the known features from a single conceptual viewpoint. This revised version was published online in September 2006 with corrections to the Cover Date.     

The origin of galactic magnetic fields

In this article it is argued that galactic magnetic fields are generated in the earliest moments of galaxy collapse. Our model proposes that provided, even if only briefly, a supermassive star is formed early on in the galaxy formation process, this star can produce a strong centrally localized magnetic field which may act as the seed field from which a galactic field can grow. In order to substantiate this model, detailed numerical calculations will be required.     

Cluster magnetic fields from galactic outflows

We performed cosmological, magnetohydrodynamical simulations to follow the evolution of magnetic fields in galaxy clusters, exploring the possibility that the origin of the magnetic seed fields is galactic outflows during the starburst phase of galactic evolution. To do this, we coupled a semi-analytical model for magnetized galactic winds as suggested by Bertone, Vogt & Enßlin to our cosmological simulation. We find that the strength and structure of magnetic fields observed in galaxy clusters are well reproduced for a wide range of model parameters for the magnetized, galactic winds and do only weakly depend on the exact magnetic structure within the assumed galactic outflows. Although the evolution of a primordial magnetic seed field shows no significant differences to that of galaxy cluster fields from previous studies, we find that the magnetic field pollution in the diffuse medium within filaments is below the level predicted by scenarios with pure primordial magnetic seed field. We therefore conclude that magnetized galactic outflows and their subsequent evolution within the intracluster medium can fully account for the observed magnetic fields in galaxy clusters. Our findings also suggest that measuring cosmological magnetic fields in low-density environments such as filaments is much more useful than observing cluster magnetic fields to infer their possible origin.     

Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.     

Open magnetic fields and the solar cycle

Models of open magnetic structures on the Sun are presented for periods near solar minimum (CR 1626–1634) and near solar maximum (CR 1668–1678). Together with previous models of open magnetic structures during the declining phase (CR 1601–1611) these calculations provide clues to the relations between open structures, coronal holes, and active regions at different times of the solar cycle. Near solar minimum the close relation between active regions and open structures does not exist. It is suggested that near solar minimum the systematic emergence of new flux with the proper polarity imbalance to maintain open magnetic structures may occur primarily at very small spatial scales. Near solar maximum the role of active regions in maintaining open structures and coronal holes is strong, with large active regions emerging in the proper location and orientation to maintain open structures longer than typical active region lifetimes. Although the use of He I 10830 Å spectroheliograms as a coronal hole indicator is shown to be subject to significant ambiguity, the agreement between calculated open structures and coronal holes determined from He I 10830 Å spectroheliograms is very good. The rotation properties of calculated open structures near solar maximum strongly suggest two classes of features: one that rotates differentially similar to sunspots and active regions and a separate class that rotates more rigidly, as was the case for single large coronal holes during Skylab.     

Studies of solar magnetic fields

An estimate of the average magnetic field strength at the poles of the Sun from Mount Wilson measurements is made by comparing low latitude magnetic measurements in the same regions made near the center of the disk and near the limb. There is still some uncertainty because the orientation angle of the field lines in the meridional plane is unknown, but the most likely possibility is that the true average field strengths are about twice the measured values (0–2 G), with an absolute upper limit on the underestimation of the field strengths of about a factor 5. The measurements refer to latitudes below about 80°.     

Studies of solar magnetic fields

In order to provide a smooth transition to a smaller aperture for the Mount Wilson daily magnetograms, a 2-step change was made, with two daily observations made using two different apertures covering an interval of several months. A comparison of these observations has made possible a check on the zero-level and calibration errors of the Mount Wilson magnetograph in recent years, and it has shown that an interval of low measured total magnetic flux resulted at least in part from an increase in the mixing of magnetic elements of the two polarities on a scale comparable with the aperture size.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.     

Studies of solar magnetic fields

Magnetic flux data from the Mount Wilson magnetograph are examined over the interval 1967–1973. The total flux in the north is greater than that in the south by about 7% over this interval, reflecting a higher level of activity in the northern hemisphere. Close to 95% of the total flux is confined to latitudes equatorward of 40°, which means that close to 95% of the flux cancels with flux of opposite polarity before it can migrate poleward of 40°. It is pointed out that a consequence of this flux distribution is that ephemeral regions must make a negligible contribution to the long-term largescale magnetic flux distribution. A broad peak in the total flux may be seen centered about one year after activity maximum in the north below 40°. In the south there is a very sharp increase in flux about the same time. In the north, several poleward migrations of flux may be seen. Two of these may correspond with the two poleward prominence migrations seen by Waldmeier. In both the north and the south there is a poleward migration of negative flux about the time of activity maximum. Poleward flux drift rates are about 20 m s^?1.     

Studies of solar magnetic fields

Solar Physics - The telescope, spectrograph, and magnetograph at the 150-ft Tower Telescope are described, and a chronology of changes in the instrumentation is given. The average magnetic field...     

High latitude solar magnetic fields

We use Kitt Peak magnetograms to measure polar magnetic fields. The polar mean absolute field increases at the same time as the polar mean field decreases. That is, the polar mean absolute field varies in phase with solar activity, in contrast to the out of phase variation of the mean polar field. We find that the polar fields have a large bipolar component even at solar minimum, with a magnitude equal to that found at low latitudes outside the active latitude bands.     

Twists and rotations of solar magnetic fields

Evidence is reviewed and extended that most, if not all, solar magnetic fields emerge as highly concentrated (4000 gauss)helically twisted flux ropes, made up of hundreds or thousands of individually twisted flux fibers. The pitch angles of the twists are estimated as 10° in the submerged flux ropes and roughly 1° in the flux fibers, but increase by large factors during and following emergence. The upward transmission of magnetic stresses and motions from the submerged flux-rope sections are major factors in solar physics. The helical twists account for the creation of sunspots and for their stability, fine structure, and mode of decay. They are basic features of the atmospheric structures, from the largest prominences and flare events down to arch filament systems and the smallest network components.     

Fine structure of solar magnetic fields

The deduction of magnetic fields from chromospheric structure is extended to active regions and transverse fields. Fields independently predicted by these rules from a high resolution H filtergram are compared with a high resolution magnetogram. The H method has the advantage over conventional magnetograms that it shows transverse fields and relates the fields to the real Sun. It has the disadvantage that higher spatial resolution is required and that it is difficult and time consuming in very complicated regions.The response of the chromosphere to magnetic fields is most consistent. Vertical field is invariably marked by bright plage, with brightness roughly proportional to the field strength (except for sunspots). All dark fibrils mark transverse fields and are parallel to field lines. All polarity changes are marked by dark fibrils, which may be transverse fibrils perpendicular to the field boundary, or filaments (prominences) which connect more distant points, and in which the field lines run nearly parallel to the boundary. The asymmetry between preceding and following polarity found by Veeder and Zirin (1970) does not exist; it was due to the low resolution of the Mount Wilson magnetograms.The complexity of active region field structure depends on the history of the region; all flux erupts in simple bipolar form, and lines of force remain connected to sibling spots until reconnection takes place. Thus the complex structure only occurs after eruption of several dipoles which reconnect. The phenomenon of inverted polarity turns out to be due to the emergence of satellite bipolar fields, where the p spot merges with the rest of the p field and the f spot appears as an included f field. Flares usually occur when the field lines from f spot reconnect from its sibling to the main spot.     

Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Observations of small-scale solar magnetic fields

Spectrograms, obtained during moments of good seeing with the high spatial resolution afforded by the 80-cm solar image at the Kitt Peak National Observatory, show the following:

1. (1)
   Magnetic fields of several hundred gauss occur in tiny areas easily as small as 500 km in extent in regions of the solar surface sometimes well removed from areas of sunspot activity.     
   
   

Fine structure of solar magnetic fields

The problem of inequality of results of longitudinal magnetic fields measured in the magnotosensetive lines FeI 5250 and FeI 5247 is investigated. The observed ratio of longitudinal components of magnetic field H ₁₁(5250)/H ₁₁(5247) is compared to the calculated for different combinations of magnetic field elements. The calculations have been made with standard model photosphere for quiet regions. It was concluded that the underestimated value of magnetic field obtained with the FeI 5250 line is explained by the presence of unresolved elements with kilogauss magnetic fields.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.     

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.