Solar magnetic fields and convection

Recent developments in solar dynamo and other theories of magnetic fields and convection are discussed and extended. A basic requirement of these theories, that surplus fields are eliminated by turbulent or eddy diffusion, is shown to be invalid. A second basic requirement, that strong surface fields are created by granule or supergranule motions, is shown to be improbable. Parker's new thin-filament dynamo, based on the Petschek mechanism, is shown to provide the alternative possibilities: either the magnetic fields halt all convection or a steady state is reached in which the fields are a tangle of long, thin filaments. From the above and other considerations it is concluded that the dynamo and related diffuse-field theories are unacceptable, that solar magnetic fields are not dominated by convection, and that all the fields emerge as strong, concentrated fields (flux ropes) which were wound and twisted from a permanent, primordial field. The discussion may, incidentally, provide the physical elements of a deductive theory of hydromagnetic convection.     

Extragalactic cosmic rays and the galactic magnetic field

The origin and behavior of cosmic rays in the Galaxy depends crucially upon whether the galactic magnetic field has a closed topology, as does the field of Earth, or whether a major fraction of the lines of force connect into extragalactic space. If the latter, then cosmic rays could be of extragalactic origin, or they could be of galactic origin, detained in the Galaxy by the scattering offered by hydromagnetic waves, etc. If, on the other hand, the field is largely closed, then cosmic rays cannot be of extragalactic origin (at least below 10¹⁶ eV). They must be of galactic origin and escape because their collective pressure inflates the galactic field and they push their way out.This paper examines the structure of a galactic field that opens initially into intergalactic space and, with the inclusion of turbulent diffusion, finds no possibility for maintaining a significant magnetic connection with an extragalactic field. Unless some mechanism can be found, we are forced to the conclusion that the field is closed, that cosmic rays are of galactic origin, and that cosmic rays escape from the Galaxy only by pushing their way out.     

Theory of the solar cycle

The properties of kinematic -dynamos are briefly reviewed. The mean field concept, including turbulent diffusivity, is defended against recent criticism. It is pointed out that although the Maunder minimum cannot be explained by kinematic dynamo theory alone, this does not invalidate dynamo theory in general. A special discussion is devoted to attempts to evaluate the coefficients of the mean field induction equation in the case of very large conductivity. The field then behaves intermittent, in the form of locally concentrated flux tubes, and the -effect and the turbulent diffusivity may be determined by asymptotic techniques or with the help of an exact solution of the non-dissipative induction equation in Lagrangian co-ordinates.Magnetic cycles of main sequence stars other than the Sun are briefly discussed. Besides rotation, the depth of the convection zone is probably the most influencial parameter for period and amplitude of the stellar cycle.Observational programmes to advance the theory of the solar cycle must include the solar magnetic and velocity fields, over the entire Sun and on all scales. In particular the angular velocity as a function of depth should be studied further with the help of the p-eigenmodes. The knowledge of luminosity, radius and (or) temperature variations with the solar cycle would also stimulate the theoretical approach.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.Mitteilung aus dem Kiepenheuer-Institut Nr. 194.     

The disk dynamo

The simplest dynamo in a thin disk is analysed. It the antisymmetric helicity function (z) (wherez is a coordinate perpendicular to the disk plane) is smooth and limited, then the conditions for generating a magnetic field and the symmetry of the resulting solutions depend only on the form of at the segment (0,h) — whereh is the half-thickness of the disk — and the value of the dimensionless dynamo numberD. When (z) does not change its sign at this segment andD>D _c (the critical dynamo number), the excitation of non-oscillating even (quadrupole) and oscillating odd (dipole) fields are possible. When (z) changes its sign at the segment indicated, non-oscillating odd magnetic fields can also be excited.The old exact solutions of the disk dynamo are studied and new ones are found. The results can be of importance when applied to the problem of the generation of a magnetic field in galactic and turbulent disks appearing around some X-ray sources.     

On The Torsional Oscillations In Babcock–Leighton Solar Dynamo Models

The torsional oscillations at the solar surface have been interpreted by Schüssler and Yoshimura as being generated by the Lorentz force associated with the solar dynamo. It has been shown recently that they are also present in the upper half of the solar convection zone (SCZ). With the help of a solar dynamo model of the Babcock–Leighton type studied earlier, the longitudinal component of the Lorentz force, L , is calculated, and its sign or isocontours, are plotted vs. time, t, and polar angle, (the horizontal and vertical axis respectively). Two cases are considered, (1) differential rotation differs from zero only in the tachocline, (2) differential rotation as in (1) in the tachocline, and purely latitudinal and independent of depth in the bulk of the SCZ. In the first case the sign of L is roughly independent of latitude (corresponding to vertical bands in the t, plot), whereas in the second case the bands show a pole–equator slope of the correct sign. The pattern of the bands still differs, however, considerably from that of the helioseismic observations, and the values of the Lorentz force are too small at low latitudes. It is all but certain that the toroidal field that lies at the origin of the large bipolar magnetic regions observed at the surface, must be generated in the tachocline by differential rotation; the regeneration of the corresponding poloidal field, B _p has not yet been fully clarified. B _p could be regenerated, for example, at the surface (as in Babcock–Leighton models), or slightly above the tachocline, (as in interface dynamos). In the framework of the Babcock-Leighton models, the following scenario is suggested: the dynamo processes that give rise to the large bipolar magnetic regions are only part of the cyclic solar dynamo (to distinguish it from the turbulent dynamo). The toroidal field generated locally by differential rotation must contribute significantly to the torsional oscillations patterns. As this field becomes buoyant, it should give rise, at the surface, to the smaller bipolar magnetic regions as, e.g., to the ephemeral bipolar magnetic regions. These have a weak non-random orientation of magnetic axis, and must therefore also contribute to the source term for the poloidal field. Not only the ephemeral bipolar regions could be generated in the bulk of the SCZ, but many of the smaller bipolar regions as well (at depths that increase with their flux), all contributing to the source term for the poloidal field. In contrast to the butterfly diagram that provides only a very weak test of dynamo theories, the pattern of torsional oscillations has the potential of critically discriminating between different dynamo models.     

The brightest blue and red stars in M31

We obtain an approximate analytic solution of a set of nonlinear model -dynamo equations. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field, is incorporated into the model. To single out the effect of the Lorentz force on the -effect, the effect of the Lorentz force on the -effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo numberN. The amplitude is proportional toN–1, while the period is almost exactly the same as the dissipation time of the unstable mode [proportional toN; note the linear oscillation period is proportional toN/(N–1) which is quite different for the solar situation whereN1].     

The circumstellar gas of sigma orionis E

In order to explain the variable H emission and the eclipse-like light variation of Ori E, we investigated the circumstellar gas trapped by the stellar magnetic field and corotating with the star. By considering the potential along the magnetic field line, we found that the gas concentrates to a potential minimum. The circumstellar gas forms either two condensations or a disk, depending on the inclination of the magnetic dipole to the stellar rotation axis. The geometrical thickness of the circumstellar disk, of about 0.2 stellar radii, and the distance from the center of the star to the inner edge of the disk, of about 3 stellar radii, were obtained. The H emission line profile at its maximum phase and the amplitude of light variation were calculated by assuming the isothermal gas in LTE with the maximum gas density which the magnetic field can hold. The model gives good agreement with observation in the low obliquity case, and also explains the phase correlation among the H emission maximum, the light minimum, and the magnetic extreme. The model, however, failed to explain the large IR excess in theM band.     

Coronal loops and active region structure

We intercompared synoptic H, Ca K, magnetograph and Skylab soft X-ray and EUV data for the purpose of identifying the basic coronal magnetic structure of loops in a typical active region and studying its evolution. We focussed on a complex of activity in July 1973, especially McMath 12417. Our principal results are: (1) Most of the brightest loops connected the bright f plage to either the sunspot penumbra or to p satellite spots; no non-flaring X-ray loops end in umbrae; (2) short, bright loops had one or both ends in regions of emergent flux, strong fields or high field gradients; (3) stable, strongly sheared loop arcades formed over filaments; (4) EFRs were always associated with compact X-ray arcades; and (5) loops connecting to other active regions had their bases in outlying plage of weak field strength in McM 417 where H fibrils marked the direction of the loops. We conclude that a typical loop brightens in response to magnetic field activity at its feet, which heats the plasma. This suggests that the loop acts as a trap for gas convected from its base.     

Solar and stellar activity: The theoretical approach

The unified sight of solar and stellar activity has revealed a worthwhile concept under several aspects, gaming in the last decade the increasing favour of observers and theorists, and the term solar-stellar connection has recently been introduced to point out the complementarity of solar and stellar observations in the background of the basic role played by the magnetic field.The great development of stellar activity observations suggests a much wider scenario than it were possible to imagine even a few years ago and stimulates theoretical work, most of which is in the framework of the - dynamo theory.Although dynamo theory seems to be plausible and successful in capturing the fundamental mechanism of solar and stellar activity, several uncertainties and intrinsic limits do still exist and are discussed together with alternative or complementary suggestions.Further, it is stressed the relevance of nonlinear problems in dynamo theory — as magnetoconvection, growth and stability of flux tubes against magnetic buoyancy, hydromagnetic global dynamos — to improve our understanding of both small and large scale interaction of rotation, turbulent convection and magnetic field, and of the transition from linear to nonlinear regime. Finally, recent dynamo models of stellar activity are critically reviewed, as to the dependence of activity indexes and cycles on rotation rate and spectral type.Open problems to be solved by future work are outlined, pointing out the role of ever increasing stellar data in widening out our comprehension of the dynamo operation modes, which seem to depend on stellar structure, rotation and age.     

HALF-WIDTH OF A SOLAR DYNAMO WAVE IN PARKER'S MIGRATORY DYNAMO

A kinematic -dynamo model of magnetic field generation in a thin convection shell with nonuniform helicity for large dynamo numbers is considered in the framework of Parker's migratory dynamo. The asymptotic solution obtained of equations governing the magnetic field has the form of an anharmonic travelling dynamo wave. This wave propagates over most latitudes of the solar hemisphere from high latitudes to the equator, and the amplitude of the magnetic field first increases and then decreases with propagation. Over the subpolar latitudes, the dynamo wave reverses; there the dynamo wave propagates polewards and decays with latitude. The half-width of the maximum of the magnetic field localisation and the phase velocity of the dynamo wave are calculated. Butterfly diagrams are plotted and analysed and these show that even a simple model may reveal some properties of the solar magnetic fields.     

The activity of stellar aggregates and the origin of cosmic rays

A concept of stellar aggregate activity is advanced. It is shown that the aggregate activity is too high in order to generate cosmic rays. Two conditions lay claim to cosmic ray primary sources: (i) a very large number of sources (10⁴), and (ii) a homogeneous distribution of sources in the Galaxy. Supernovae do not satisfy both those conditions, but stellar aggregates do. The total interstellar medium of the aggregate identifies with a supernova remnant and possesses properties favourable for the acceleration of cosmic rays up to a high energy by statistical mechanisms. The direct suppliers of primary cosmic rays are the flare stars in the aggregates. From the point of view of energetic resources as well as the energetic consistency of cosmic rays, aggregates are equivalent with supernova remmants. The aggregate must also be the source of gamma-rays. The usual UV Cet-type flare stars in the Sun's neighbourhood do not play any role as sources of primary cosmic rays.The aggregate conception connects the very fact of the existence of cosmic rays with the continued star-formation process in Galaxy.     

Homogeneous metagalactic origin of cosmic rays

Starting with the hypothesis that cosmic rays are evenly distributed in the metagalaxy, it is shown that the flux of the electron-positron component, which is produced through --e decays, following the nuclear collisions of the cosmic ray beam with the intergalactic medium, takes <-4×10¹⁶ sec to reach steady state. The corresponding value of the flux of thepositron component and its implications regarding the homogeneous model of the metagalactic origin of cosmic rays are discussed.On leave from Tata Institute of Fundamental Research, Bombay, India.     

Suprathermal grains: On intergalactic magnetic fields

Charged dust grains of radiia3×10^–63×10^–5 cm may be driven out of the galaxy due to radiation pressure of starlight. Once clear of the main gas-dust layer, dust grains may then escape into intergalactic space. Such grains are virtually indestructible-being evaporated only during galaxy formation. The dust grains, once injected into the intergalactic medium, may acquire suprathermal energy, thus suprathermal grains in collision with magnetized cloud by the Fermi process. In order to attain relativistic energy, suprathermal grains have to move in and out (scattering) of the magnetic field of the medium. It is now well established that high energy cosmic rays are of the order 10²⁰ eV or more. We have speculated that these high energy (>-10¹⁸ eV) cosmic ray particles are charged dust grains, of intergalactic origin. This is possible only if there exists a magnetic field in the intergalactic medium.     

Suprathermal Grains: Origin of primary cosmic rays

Charged dust grains of radiia3×10^–6 cm could be a help in understanding the production of primary cosmic ray particles in extensive air showers (EAS). A two-stage acceleration mechanism is proposed in order to accelerate dust grains up to relativistic energy. In the first stage, dust grains acquire suprathermal energy (Suprathermal Grains) by the Fermi mechanism. In the second stage, suprathermal grains attain relativistic energy by the Alfvén magnetic pumping mechanism yielding the primary cosmic ray particles. Ionization loss has been considered to be a most important loss mechanism for charged dust grains in a fully ionized medium. It is suggested that graphite dust grains of intergalactic origin may be responsible for high energy (>10²⁰ eV) cosmic rays.     

Plasma wave propagation in the neighborhood of a magnetic neutral point

A linearized magnetohydrodynamic formalism is used to examine the propagation in two dimensions of transverse waves in a plasma in which is embedded a curl-free magnetic field. Only waves of frequency less than the ion cyclotron frequency are considered. The behavior of a wave packet near the magnetic neutral point is deduced from the general solution to the problem, which is found in terms of Bessel functions whose order is frequency dependent. It is shown that a disturbance propagates through the medium with a group velocity that decreases from the speed of light at large distances from the neutral point to zero at the neutral point, and that the amplitudes of the velocities associated with the disturbance diverge there. It is suggested that the stagnation of waves near the origin and the deformation of the magnetic field resulting from the large plasma-flow velocities may provide a clue to the formation of the magnetic neutral sheet required by several flare theories and a theory of the acceleration of cosmic rays.     

Stockert's chimney — A galactic fountain

A new type of galactic outflow phenomenon has been discovered and published under the name of thermal spur by Mülleret al. (1987). It is argued that this outflow consists of relativistic pair plasma with an admixture of partially ionized hydrogen and cosmic rays, escaping from a large Hii region. This chimney serves as a substantial leak for the cosmic rays, i.e., may be an essential part of the galactic foundtain.     

Solar magnetic fields and convection

Solar meridional drift motions are vitally important in connection with the origin of magnetic fields, the source of differential rotation, and perhaps convection. A large body of observational evidence is collated with the following conclusions. (i) Sunspot motions reveal latitudinal drifts (Figures 2 and 3) of a few metres per second which vary with latitude and have a strong 11-yr periodicity. There may also be a 22-yr component polewards during even cycles and equatorwards during odd. (ii) Various other tracers, all basically magnetic structures, show the 11-yr drifts at mid- and high latitudes up to the polar caps, motion being polewards during the three years starting just before minimum activity (Figure 4). (iii) The earlier evidence for giant cells or Rossby-type waves is shown to be merely misinterpretation of the hydromagnetic motions of tracers. Evidence against such giant eddies is found in the great stability of other tracer structures. (iv) From the various tracer motions a four cell axisymmetric meridional drift system is determined (Figure 5 (b)) with an 11-yr period of oscillation and amplitude a few metres per second. (v) These meridional oscillations must be a basic component of the activity cycle. They add to the difficulties of the dynamo theory, but may explain the emergence of stitches of flux ropes to form relatively small bipolar magnetic regions. (vi) The two cells also throw light on thetwo sunspot zones in each hemisphere, discussed earlier by Becker and by Antalová and Gnevyshev.     

‘Dead’ pulsars: Cosmic-ray sources

Dead pulsars outnumber live pulsars by a factor of 10⁴. It is estimated that there are 3×10⁹ of them in our Galaxy. The exospheres of the atmosphere of dead pulsars are characterised by cosmic-ray energies per particle, as the result of accretion of cold particles from interstellar space. Velocities of particles in the exosphere tend to be Maxwellianised by collisions there. The temperature of the exosphere from which particles escape is of the order of 10¹² K while the temperature of the photosphere closer to the surface of the pulsar is of the order of 10⁷ K. Collisions in the exosphere result in Jeans's type escape of cosmic rays with GeV energies at infinity. Two braod ranges of conditions for the exospheres are considered (a) with no magnetic fields involved, and (b) with magnetic fields. Similar conclusions are reached regarding the escape of cosmic rays. Conditions are delineated such that the exospheres of dead pulsars might be major sources of cosmic rays.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

On the generation of the large-scale and turbulent magnetic fields in solar-type stars

It is thought that the large-scale solar-cycle magnetic field is generated in a thin region at the interface of the radiative core (RC) and solar convection zone (SCZ). We show that the bulk of the SCZ virogoursly generates a small-scale turbulent magnetic field. Rotation, while not essential, increases the generation rate of this field.Thus, fully convective stars should have significant turbulent magnetic fields generated in their lower convection zones. In these stars the absence of a radiative core, i.e., the absence of a region of weak buoyancy, precludes the generation of a large-scale magnetic field, and as a consequence the angular momentum loss is reduced. This is, in our opinion, the explanation for the rapid rotation of the M-dwarfs in the Hyades cluster.Adopting the Utrecht's group terminology, we argue that the residual chromospheric emission should have three distinctive components: the basal emission, the emission due to the large-scale field, and the emission due to the turbulent field, with the last component being particularly strong for low mass stars.In the conventional dynamo equations, the dynamo frequencies and the propagation of the dynamo wave towards the equator are based on the highly questionable assumption of a constant . Furthermore, meridional motions, a necessary consequence of the interaction of rotation with convection, are ignored. In this context we discuss Stenflo's results about the global wave pattern decomposition of the solar magnetic field and conclude that it cannot be interpreted in the framework of the conventional dynamo equations.We discuss solar dynamo theories and argue that the surface layers could be essential for the generation of the poloidal field. If this is the case an -effect would not be needed at the RC-SCZ interface (where the toroidal field is generated). The two central problems facing solar dynamo theories may the transport of the surface poloidal field to the RC-SCZ interface and the uncertainty about the contributions to the global magnetic field by the small-scale magnetic features.Visitor, National Solar Observatory, National Optical Astronomy Observatories.The National Optical Astronomy Observatories are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.     

The acceleration and propagation of solar cosmic rays as deduced from the relative abundance of protons to helium nuclei

Except for protons, the chemical composition of solar cosmic rays is very similar to the abundance of the elements at the photosphere of the Sun. If we consider the relative abundance ratio of protons to -particles (P/) at constant rigidity, this ratio is highly variable from one solar cosmic ray event to another. This ratio observed at the Earth, however, decreases monotonically with time from the onset of solar flares and, furthermore, is dependent on the heliocentric distance of the parent flares from the central meridian of the solar disk. P/'s which have been measured before the onset of SC geomagnetic storms change from 1.5 to 50 or more, being a function of the westward position of the source from the east limb of the Sun. These variations with respect to time and heliocentric distance suggest that the propagation of solar cosmic rays is strongly modulated in the interplanetary space. The major part of the -particles seem to propagate as if they are trapped within the magnetic clouds which produce SC geomagnetic and cosmic ray storms at the earth.The chemical composition and rigidity spectra of solar cosmic rays suggest that solar cosmic rays are mainly accelerated by the Fermi mechanism in solar flares. The observed variation of P/'s is produced mainly through the difference between the propagation characteristics of protons and -particles.NAS-NRC Associate with NASA.