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.     

Spontaneous Formation of Magnetic Flux Concentrations in Stratified Turbulence

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma ?? are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L ²/?? _t, where ?? _t is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number.     

The Hanle effect and the diagnostics of turbulent magnetic fields in the solar atmosphere

The theory of the Hanle effect is used to interpret the linear polarization measured in a number of spectral lines on the solar disk near the heliographic north and south poles, in search for a turbulent magnetic field in the solar atmosphere. The Hanle depolarization is separated from a number of other effects, including collisional depolarization and scattering geometry. Although the main aim of the paper is to elucidate the physics of the Hanle effect as applied to the Sun, our results indicate the existence of hidden or turbulent magnetic flux near the temperature minimum of the solar atmosphere, with a field strength between 10 and 100 G. This field is hidden in the sense that it is not seen in measurements of the longitudinal Zeeman effect (solar magnetograms). It carries more total magnetic flux than the kG network fields.     

Study of interplanetary magnetic field with Ground State Alignment

We demonstrate a new way of studying interplanetary magnetic field—Ground State Alignment (GSA). Instead of sending thousands of space probes, GSA allows magnetic mapping with any ground telescope facilities equipped with spectropolarimeter. The polarization of spectral lines that are pumped by the anisotropic radiation from the Sun is influenced by the magnetic realignment, which happens for magnetic field (<1 G). As a result, the linear polarization becomes an excellent tracer of the embedded magnetic field. The method is illustrated by our synthetic observations of the Jupiter’s Io and comet Halley. Polarization at each point was constructed according to the local magnetic field detected by spacecrafts. Both spatial and temporal variations of turbulent magnetic field can be traced with this technique as well. The influence of magnetic field on the polarization of scattered light is discussed in detail. For remote regions like the IBEX ribbons discovered at the boundary of interstellar medium, GSA provides a unique diagnostics of magnetic field.     

Radial mixing in the outer Milky Way disc caused by an orbiting satellite

The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.     

Dynamic confinement of jets by magnetotorsional oscillations

Many quasars and active galactic nuclei (AGN) appear in radio, optical and X-ray maps as bright nuclear sources from which emerge single or double long, thin jets. When observed with high angular resolution, these jets show evidence of structure, with bright knots separated by relatively dark regions. High percentages of polarization, sometimes more then 50 per cent, indicate the non-thermal nature of the radiation, which is well explained as the synchrotron radiation of the relativistic electrons in an ordered magnetic field.
A strong collimation of jets is probably connected with ordered magnetic fields. The mechanism of magnetic collimation first suggested by Bisnovatyi-Kogan et al. was based on the initial charge separation, which led to the creation of an oscillating electrical current, which in turn produced an azimuthal magnetic field, preventing jet expansion and disappearance. Here we consider magnetic collimation associated with the torsional oscillations of a cylinder with an elongated magnetic field. Instead of initial blobs with charge separation, we consider a cylinder with a periodically distributed initial rotation around the cylinder axis. The stabilizing azimuthal magnetic field is created by torsional oscillations, meaning that charge separation is unnecessary. An approximate simplified model is developed, and an ordinary differential equation is derived and solved numerically, making it possible to estimate quantitatively the range of parameters for which jets may be stabilized by torsional oscillations.     

Active Region Formation through the Negative Effective Magnetic Pressure Instability

The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.     

Hydromagnetic unsteady flow due to an unsteady plate

The unsteady flow near an infinite flat plate, which is oscillating harmonically in its own plane, is studied in the presence of a magnetic field subjected to suction or injection. The magnetic field is perpendicular to the plate and the flow of viscous incompressible and electrically conducting fluid is regarded as being initially at rest. Exact solutions for velocity and skin-friction are obtained for the magnetic field fixed to the fluid or to the plate.     

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.     

The dynamic magnetic quiet Sun: physical mechanisms and UV signature

The changes in the Sun occurring at human time-scales can be pinned down to the presence of magnetic fields. These fields determine the structure of the outer solar atmosphere and, therefore, they are responsible for all the energetic part of the solar spectrum, including the UV. Our understanding of the magnetic fields existing at the base of the atmosphere has changed during the last years. The new spectro-polarimeters reveal an ubiquitous magnetic field, present even in the quiet regions. They are widespread and of complex topology, containing far more (unsigned) magnetic flux and magnetic energy that all traditional manifestations of solar activity. These so-called quiet Sun magnetic fields are the subject of the contribution. I summarize their main observational properties, as well as the models put forward to explain them. According to the common wisdom, they may be generated by a turbulent dynamo driven by convective motions. Their true physical role is not understood yet, but it may be consequential both for the Sun (e.g., in determining the structure of the quiet corona), and for other astronomical objects (e.g., if a turbulent dynamo operates in the Sun, the same mechanism provides a very efficient mean of creating surface magnetic fields in all stars with convective envelopes). I discuss the impact of the quiet Sun fields on the transition region and corona, trying to point out the UV signatures of those fields.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

太阳剩余磁场研究进展

太阳剩余磁场是指形成于太阳主序星阶段之前，深藏在太阳辐射核内部的原始磁场。由于太阳内部高电导率和准静态等因素，其剩余磁场耗散相当缓慢，而得以保留至今。太阳剩余磁场的存在不仅能够解释太阳活动的很多不对称性现象，如南北不对称性、活动经度与活动穴、低纬度冕洞和Maunder极小期等，还能通过改变自激发发电机模型的边值条件而影响整个太阳表面磁场的分布与演化。从观测结果和理论模型两方面评述了太阳剩余磁场的研究成果及最新进展，并简单讨论了进一步努力的方向。     

Dynamo mechanism for turbulent wave in celestial bodies

It is well known that under cosmic conditions the various modes of plasma turbulence waves (including MHD waves) are easily excited. In this paper we are trying to show that the turbulent wave also generates a source-term for the magnetic induced equations as does the turbulent fluid with nonzero helicity. By expanding the turbulent field in Fourier series, we have obtained dynamo equation for turbulent wave and a reasonable solution which indicates that the poloidal field may be built-up in the turbulent source region. Perhaps, we may think that the poloidal field of Equation (9) is the analytical form of the magnetic field in a turbulent source region of celestial bodies.     

Hydromagnetic flow near an oscillating wall

The flow of a viscous incompressible and electrically conducting fluid produced by harmonically oscillating wall of infinite extent in presence of a transverse magnetic field is considered. Exact solutions for velocity, induced magnetic field, electrical current density and skin-friction are obtained when the magnetic Prandtl number is unity. It is shown that the velocity has a phase lag with respect to the oscillations of the wall. This phase lag is found to be significantly affected by the applied magnetic field.On study-leave from Defence Science Laboratory, Delhi, India.     

Similarities and Differences between Coronal Holes and the Quiet Sun: Are Loop Statistics the Key?

Coronal holes (CH) emit significantly less at coronal temperatures than quiet-Sun regions (QS), but can hardly be distinguished in most chromospheric and lower transition region lines. A key quantity for the understanding of this phenomenon is the magnetic field. We use data from SOHO/MDI to reconstruct the magnetic field in coronal holes and the quiet Sun with the help of a potential magnetic model. Starting from a regular grid on the solar surface we then trace field lines, which provide the overall geometry of the 3D magnetic field structure. We distinguish between open and closed field lines, with the closed field lines being assumed to represent magnetic loops. We then try to compute some properties of coronal loops. The loops in the coronal holes (CH) are found to be on average flatter than in the QS. High and long closed loops are extremely rare, whereas short and low-lying loops are almost as abundant in coronal holes as in the quiet Sun. When interpreted in the light of loop scaling laws this result suggests an explanation for the relatively strong chromospheric and transition region emission (many low-lying, short loops), but the weak coronal emission (few high and long loops) in coronal holes. In spite of this contrast our calculations also suggest that a significant fraction of the cool emission in CHs comes from the open flux regions. Despite these insights provided by the magnetic field line statistics further work is needed to obtain a definite answer to the question if loop statistics explain the differences between coronal holes and the quiet Sun.     

Magnetic flux separation in photospheric convection

Three-dimensional non-linear magnetoconvection in a strongly stratified compressible layer exhibits different patterns as the strength of the imposed magnetic field is reduced. There is a transition from a magnetically dominated regime, with small-scale convection in slender hexagonal cells, to a convectively dominated regime, with clusters of broad rising plumes that confine the magnetic flux to narrow lanes where fields are locally intense. Both patterns can coexist for intermediate field strengths, giving rise to flux separation: clumps of vigorously convecting plumes, from which magnetic flux has been excluded, are segregated from regions with strong fields and small-scale convection. A systematic numerical investigation of these different states shows that flux separation can occur over a significant parameter range and that there is also hysteresis. The results are related to the fine structure of magnetic fields in sunspots and in the quiet Sun.     

Unsteady hydromagnetic rotating flow near an oscillating plate

The three-dimensional flow of a viscous incompressible electrically conducting fluid near an infinite plate (or wall) of non-conductor, which is oscillating harmonically in a uniform rotating medium, is studied in the presence of a uniform magnetic field. The impressed uniform magnetic field is perpendicular to the plate and the induced magnetic field is considered. Exact solution of this problem is obtained for the velocity and magnetic fields. Neglecting the induced magnetic field we readily obtain the results of all the previous investigations. The effects of the rotation and the magnetic field are comparable with one another and are discussed for the whole problem. Also, the drag and the lateral stress on the plate are discussed.     

Heliospheric propagation of galactic cosmic rays depending on the scattering characteristics of the turbulent interplanetary magnetic field

The effect of the solar wind on the spectrum of cosmic rays accelerated in the Galaxy is studied. The coefficient of cosmic-ray diffusion in the interplanetary turbulent magnetic field is assumed to be independent of the particle energy and a power-law function of the distance from the Sun. The particle spectrum at the heliospheric boundary is specified as a power-law function of the total particle energy.     

The dynamo theory of plasma turbulence wave in rotating celestial bodies

The various modes of plasma turbulence waves (including MHD waves) are easily excited under cosmic circumstances. In this paper, if we consider that the celestial bodies rotate, there is a source term generated for the magnetic induced equation by the excited plasma turbulence waves. If we expand the turbulent field in the Fourier series and include rotation velocity, the dynamo equation for turbulent waves is obtained. We have also obtained the solutions of various wave forms corresponding to different rotation velocities and then we significantly discuss the magnetic fields in the Sun, planets, and other celestial bodies.     

Mechanism of cyclically polarity reversing solar magnetic cycle as a cosmic dynamo

We briefly describe historical development of the concept of solar dynamo mechanism that generates electric current and magnetic field by plasma flows inside the solar convection zone. The dynamo is the driver of the cyclically polarity reversing solar magnetic cycle. The reversal process can easily and visually be understood in terms of magnetic field line stretching and twisting and folding in three-dimensional space by plasma flows of differential rotation and global convection under influence of Coriolis force. This process gives rise to formation of a series of huge magnetic flux tubes that propagate along iso-rotation surfaces inside the convection zone. Each of these flux tubes produces one solar cycle. We discuss general characteristics of any plasma flows that can generate magnetic field and reverse the polarity of the magnetic field in a rotating body in the Universe. We also mention a list of problems which are currently being disputed concerning the solar dynamo mechanism together with observational evidences that are to be constraints as well as verifications of any solar cycle dynamo theories of short and long term behaviors of the Sun, particularly time variations of its magnetic field, plasma flows, and luminosity.