When measuring the magnetic fields of sunspots the astronomer assumes that the magnetic field revealed by the inverse Zeeman effect is the same as if the splitting were produced by emission lines instead of absorption lines. No doubt this is in general a very fair approximation, but we have reason to remember sometimes that line absorption in the presence of magnetic fields is a very complicated process. In the immediate neighbourhood of absorption lines effects of magnetic rotation of the plane of polarization and magnetic double refraction may appear in the spectrum.

Relatively complete summaries of recent theoretical work in the field of stellar magnetism have been given by Cowling[1] and Elsasser[2, 3, 4]. For this reason the present survey does not aim at completeness, but is devoted instead to the following three outstanding problems in the field: (1) the formation of stars in the presence of an interstellar magnetic field; (2) the influence of convection currents on a stellar magnetic field; (3) the nature of magnetic variable stars. Study of these problems illustrates the type of difficulties encountered in theories of stellar magnetism.

Some aspects of the problem of magnetic fields in the interstellar space and in the nebulae are discussed in this paper. Our observational basis are the numerous photographs of the nebulae in Hα and other rays, taken with high-speed 450 and 640 mm cameras.

The greatly elongated shape of many emission nebulae is interpreted as a result of three factors, the effect of the magnetic field, the macroscopic motions in these nebulae (including the tendency to expand) and the high electrical conductivity of matter. The expansion of nebulae is to be generally accompanied by the considerable decrease in brightness (roughly about d–5), but if the expansion is only in one direction, owing to the presence of a regular magnetic field, the brightness decreases much more slowly (roughly about d–2) and the nebulae remain visible for a longer time. The filamentary structure, which is very often inherent to the elongated nebulae, is, probably, an additional factor of a longer visibility of the nebulae under consideration. The great lengthening of nebulae may be reached in the period of the order of 106 years.

In the dark nebulae the matter seems to be electrically conductive and the macroscopic motions of the order of 1–2 km/sec are present there, so that there are reasons to suggest that the magnetic field is also responsible for the elongated shape of many dark nebulae. One may prove that the observed elongated shape of dark and emission nebulae could not be caused by differential galactic rotation.

This paper is a development of the hypothesis, suggested earlier by the author, namely that novae possess a large general magnetic field. This hypothesis explains the following facts: (a) effects of the retardation of matter in novae before light maximum, (b) a preferential ejection of matter from novae in two diametrically opposite directions during an outburst, and (c) formation of rings and equatorial belts after light maximum, observed in N Aql 1918 and N Her 1934. These rings and belts are formed due to the fact that the general magnetic field of new stars deflects condensations of continuous ejection (the diffuse-enhanced and Orion spectra) towards the equator.

Magnetic fields inside novae must be ‘tangled’. This explains (a), as well as the difference between cases (b) and (c).

The structure of envelopes, ejected by novae, must reflect the presence of tangled magnetic fields. According to G. A. Shajn this is confirmed for super-novae, the envelopes of which may be studied in detail.

The stars in the Double Cluster in Perseus whose angular distance is small have similar polarization and similar colour excesses. Quantitative description of this effect is the purpose of this paper.

Certain stars are known to be periodic magnetic variables, and to show synchronous changes in line strength and radial velocity. The hypothesis has been made that the atmosphere of such a star is in rigid rotation, and that it is characterized by a permanent magnetic field and associated abundance irregularities. The magnetic potential and the local equivalent widths have been developed in spherical harmonics, and the Laplace coefficients of these expansions have been related to the Fourier coefficients of the observed curves. The theory has been applied to the star HD 125248 in an attempt to verify the original hypothesis and to map the magnetic fields and abundance anomalies over the stellar atmospheres.

A modified discussion of surface nuclear reactions in magnetic stars is given. The anomalous abundance effects found in magnetic stars are briefly described. It is suggested that the processes of particle acceleration are similar to those taking place in the solar atmosphere which give rise to the cosmic ray bursts observed by Wild, Roberts, and Murray, and to the solar component of cosmic radiation. Calculations of the rate of loss of energy following particle acceleration suggests that the duration of the hot spot is 1 ≲ sec. It is estimated that in the region of acceleration (p, n) reactions will enable a ratio nn/np ⋍ 10–2–10–3 to be built up. The majority of these neutrons will diffuse from the excited regions and form deuterium in the quiescent atmosphere. This deuterium will be continuously built up and re-acceleration will lead to the release of neutrons, some of which will be captured by the Fe group, eventually giving rise to the observed anomalous abundances of the heavy elements. Also the reaction H(d, γ) He3 may give rise to the formation of some He3.

Since 1952 a total of 635 magnetograms of the sun have been obtained in a systematic investigation of weak magnetic fields in the photosphere. The frequent records give the location, polarity, and intensity of weak fields down to a fraction of 1 gauss, although with resolution limited to about 0·04 of the solar diameter.

Confirmation of previously reported results in 1954 comes from continuation of the series and from observations with a second, improved magnetograph on Mount Wilson. Three types of field pattern are found: (1) the poloidal field in high heliographic latitudes, consistently positive in the north, negative in the south, with intensity of the order of 1 gauss; (2) BM (bipolar magnetic) regions, often weak and extended, but which when strong are associated with plages, spots, flares, coronal emission, chromospheric fine structure, and filaments; and (3) UM (unipolar magnetic) regions, rather extended and weak, occurring in low latitudes, and associated in time with 27-day recurrent geomagnetic storms and cosmic-ray fluctuations. Attention is directed to the probable disposition of the magnetic flux in the high atmosphere and in interplanetary space, consistent with the observed magnetic areas and with the restriction div H = 0.

Alfvén has argued that the interpretation of the small Zeeman displacements is meaningless and irrelevant because the rather strong turbulent fields presumed to prevail in granules might be coupled systematically, in respect to magnetic polarity, with the intensity of the absorption lines used for measurement. But this would produce a bias, with a shift of zero point of magnetic intensity, for all observed fields on the disk, and no such bias is observed. The measurements, while limited in resolution, are on an absolute scale, and show, for the ‘quiet sun’, vast areas with only small random fields no greater than a few tenths of 1 gauss.

It is shown in outline by a discussion of the equation of motion in all its components and by taking regard of the geometrical properties of turbulent exchange, that in general the state of pure rotation (without meridional circulations) is not a possible stationary state of motion for convective zones of stars.

The observational data on the magnetic fields and the physical parameters in sunspots indicate in a qualitative way how the magnetic lines of force run relative to the isobaric surfaces. If matter is confined to move only along the lines of force it is shown that for sufficient tilt between these lines and the isobars, matter will be accelerated outward along the lines of force. The flow corresponding to this forced convection works as a cooling cap for the core of the spot. It is indicated how a stationary state may be reached with the outward velocity adapted to the temperature difference between the spot and the photosphere.

The constitution of stationary single sunspots of circular shape is considered. Account is taken of the mechanical effects of the magnetic field, including those which arise from the curvature of the lines of force. To make the system of magneto-hydrostatic equations manageable, it is assumed that the relative distribution of the vertical component of the magnetic field is the same across the flux-tube of the spot in all depths. Preliminary results indicate that suppression of convective energy transport by the magnetic field in those depths in which ionization of hydrogen takes place, will give the essential observable properties of sunspots, relatively independent on the asumptions about the physical processes in greater depths. There the physical properties of matter can deviate but very little from those of the indisturbed hydrogen convection zone.

The shapes of coronal features are discussed, on the basis that they are indicative of the configurations of the magnetic fields. Some considerations about the strength of the fields are advanced, and the forces that must be responsible for streamers and for the quiet corona are discussed. The magnetic fields would seem to dominate over all inertial hydrodynamic forces, leaving only such magnetic configurations as can be set up by variations of the gas pressure.

It is pointed out that the model of mutually penetrating ideal charged and neutral gases can be used with particular success to describe the motion of an extremely rarefied plasma. As a simplest instance of application of such a model, the acceleration of totally ionized gases in crossed electric and magnetic fields is considered. It is shown that the general solution of the problem in two limiting cases is either magneto-hydrodynamic or the free charge solution.

The magnetic field outside the sun (interplanetary magnetic field) is certainly far from a dipole field. A model of it has recently been suggested (Tellus, 8, 1, 1956). This model is in agreement with cosmic ray and magnetic storm data and reconcilable with the coronal ray structure. Some possibilities to check the model are discussed.

The evidence in favour of a corpuscular theory of magnetic storms is briefly reviewed and reasons given for believing that the stream must be neutral but ionized and carry no appreciable current. It is shown that under suitable conditions the stream is able to pass freely through a solar magnetic field; the stream may also be able to carry away with it a part of this field. However, because of geometrical broadening of the stream during its passage from the sun to the earth, the magnetic field imprisoned in the gas may be wellnigh unobservable near the earth.

The nature, composition and dimensions of the stream near the earth are discussed and it is concluded that on arrival the stream will present very nearly a plane surface to the earth if undistorted by the magnetic field.

Because of its large dimensions, the stream will behave as if it were perfectly conducting. During its advance in the earth's magnetic field the currents induced in the stream will therefore be practically confined to the surface. The action of the magnetic field on this current is to retard the surface of the stream which being highly distortible will become hollowed out. Since the stream surface is impervious to the interpenetration of the magnetic tubes of force, these will be compressed in the hollow space. The intensity of the magnetic field is thereby increased and this increase is identified with the beginning of the first phase of a magnetic storm. This increase will be sudden, as observed, owing to the rapid approach of the stream to the earth.

The distortion of the stream surface is discussed and it is pointed out that two horns will develop on the surface, one north and the other south of the geomagnetic equator. Matter pouring through these two horns will find its way to the polar regions.

The main phase of a magnetic storm seems most simply explained as due to a westward ring-current flowing round the earth in its equatorial plane. Under suitable conditions such a ring-current would be stable if once set up. The mode of formation of the ring is, however, largely conjectural. The possibility that the main phase may be of atmospheric origin is also briefly considered. It is shown that matter passing through the two horns to the polar regions could supply the energy necessary for the setting up of the field during the main phase. The magnetic evidence in favour of such a hypothesis, however, seems wanting.

The main features of the electric field theory are outlined. The theory should be considered as a first approximation. The validity of the approximations and assumptions introduced is discussed.

Some model experiments on the theory are described. It is impossible to construct an entirely true model of nature in the laboratory. The similarities and differences between nature and model are discussed.

The mechanism of the model seems to be described very well by the theory. Some experimental results, which because of the complicated phenomena cannot be predicted by the theory, are compared with observations in nature. As far as we can see at present, the agreement between nature and model is astonishingly good.

Three topics are discussed dealing with interplanetary phenomena. They are: (i) sudden commencement of magnetic storms[1]; (ii) main phase of magnetic storms[2]; (iii) cosmic ray effects associated with solar corpuscular emission[3].

To explain the sudden commencement(SC) of magnetic storms, the reverse sudden commencement (SC*), and the pre-SC disturbances, we invoke the following model: The solar eruption produces a shock-wave which arrives at the earth 22–34 hr later. High velocity particles having a smaller interaction precede the shock-wave and cause the pre-SC bay-like disturbances at high latitudes. The shock-wave itself is retarded by the body forces produced by the geomagnetic field, but speeds up as it enters the auroral zones. In pushing out lines of force it creates the polar SC* events. Charge separation in the shock-wave produces the driving force for the SC currents which flow in the atmosphere (in accordance with Vestine's analysis).

The storm decrease is produced by the high velocity particles following the shock-wave (up to 9 hr later) which enter because of field perturbations into the normally inaccessible Störmer regions around the dipole. Here they are trapped and will drift producing the ring-current which gives rise to the storm decrease. Particles with small pitch angle, however, can reach the earth's atmosphere and contribute to aurora, the air-glow, and ionospheric ionization. These particles are replenished by perturbations produced by solar influences having a 27-day recurrence. Many other particles are absorbed or scattered out of the trapping regions so that their number diminishes rapidly in a day or so, as does the magnetic storm decrease.

The model thus attempts to explain for the first time the cause of the reverse sudden commencement events (SC*), the atmospheric nature of SC, the delay between SC and the main phase, the formation and decay of the ring-current. A by-product is auroral particle acceleration by a shock-wave[4].

New experimental tests are suggested by the model: (i) Acoustic observations with balloons to look for the shock-wave penetrating into the atmosphere in the auroral zones. (ii) Observations with rockets or satellites to establish the location of the SC and main phase currents. (iii) Measurements of the nature and energy of the auroral particles[5].

It is suggested that the cosmic ray decrease occurring with magnetic storms (Forbush events), as well as the 27-day decreases of cosmic ray intensity, are modulation effects produced primarily by the deceleration of cosmic rays in interplanetary space due to the expansion of turbulent gas clouds from the sun. The detailed mechanism depends on a statistical decrease of the initially high turbulent fields and can therefore be called an ‘inverse Swann effect’ or ‘inverse Fermi effect’. The cosmic ray intensity variation during the solar cycle is accounted for as the cumulative effect of this mechanism which operates in connexion with emission of solar gas. In this way it is possible also to account for the decrease lasting six months observed by Forbush starting in February 1946. Some experimental tests are suggested to discriminate between different theories for the origin of cosmic ray time variations[3].

The amplitude of the average 27-day wave in cosmic ray intensity, at Huancayo, Peru, and its phase relative to that for the 27-day wave in international magnetic character figure (ICF) is determined from results of harmonic analysis of data for each of 246 intervals (or solar rotations) of 27 days. From these data, the variability of which is essential for tests of statistical significance, the amplitude of the average 27-day wave in cosmic ray intensity and its phase relative to that in geomagnetic activity is determined for each of three groups of solar rotations selected according to the average of the amplitudes of the 27-day waves in magnetic activity. A fourth group contained only 27-day intervals in which large cosmic ray decreases occurred. Relative to that in magnetic activity, the phase of the 27-day wave in cosmic ray intensity is found for the averages, to be the same for the four groups.

The maxima of the average cosmic ray waves occur about 1·5 days after the minima of the corresponding waves in ICF. In general, the amplitude of the average 27-day wave in cosmic ray intensity, in the co-ordinate system in which its phase is relative to that of the 27-day wave in ICF tends to be greater for the selected groups of rotations with larger average ICF amplitudes. For most years near sunspot minimum the amplitude of the 27-day cosmic ray wave does not differ significantly from zero.

Bartels found for 27-day waves in ICF the effective number of statistically independent 27-day waves for N successive solar rotations to be N/3; the number found for cosmic ray intensity is N/2. Thus, on the average the 27-day recurrence tendency is less for cosmic ray intensity than for magnetic activity.

The Chree method of analysis has been adopted for the analysis of the Ionization Chamber data for Huancayo, Cheltenham and Godhavn for 1946 and for the former two stations for 1945. The same procedure is adopted for the planetary index Kp also.

The cosmic ray minimum (or maximum) precedes the minimum (or maximum) of Kp by about 4–5 days. It is also observed that the relative decrease in cosmic ray intensity per day, – ΔI/(I. Δt), follows the changes in Kp in a general way, and hence the electric field as would be expected from the consideration of the theory of emission of beams of particles from the sun with the associated frozen magnetic field and the electric field arising due to polarization.

The principal characteristics for changes of cosmic ray intensity as a function of time and primary particle energy are reviewed for those intensity variations which are thought to be of non-terrestrial origin. These variations are either (a) temporary increases of cosmic ray intensity arising from the de novo production of cosmic ray particles in the vicinity of the sun in association with some solar flares, or (b) the modulation of extra-solar cosmic radiation within the interplanetary volume by a modulation mechanism related to solar activity.

The study of these variations for low-energy cosmic ray particles is also a unique tool for the investigation of interplanetary magnetic fields and other properties of interplanetary space. As an example, the cosmic ray events associated with the giant solar flare of 23 February 1956 have been studied. The experimental evidence shows that interplanetary magnetic fields must exist for the storage and redistribution of the solar flare cosmic ray particles. A more specific model indicates that disordered magnetic fields lie mainly beyond the orbit of the earth and that diffusion through these irregular magnetic fields is the prominent mechanism for particle storage. In addition, this cosmic ray intensity increase was fortunately superposed in such a way upon a change of intensity arising from a modulation mechanism that it is possible to restrict the kinds of models which account for modulation of cosmic ray intensity within the interplanetary volume.