A typical stellar spectrogram shows a vast number of spectral lines. Each of these has its characteristic shape and strength which must, in some way, reflect the structure of the atmosphere in which the radiation arose. It seems reasonable that from all this profile data we should be able (and with considerable redundancy) to infer a good deal about the physical structure of the radiating gas, and a major effort has correspondingly been devoted to clarifying the physical basis of spectral line formation, i.e., exactly how the atmospheric structure and the atomic properties are reflected in the line profiles. This problem, however, is far from solved : Few, if any, of the profiles of strong lines can be predicted in detail from model atmospheres, nor have analyses of the profiles yielded unambiguous data on the atmospheric structure. Indeed, as recently as 1967, the participants at a conference in Bilderberg (Holland) concluded that no data at all which had been obtained from line profile analyses was worthy of inclusion in specifying the solar atmospheric model. Evidently, then, the problem of line formation is not trivial ; in this paper we discuss some of the difficulties and review the not inconsiderable progress which has been made in this area of astrophysical research.

It has long been known that Fraunhofer lines show variations in intensity from place to place over the Sun’s surface, these being particularly noticeable in spectroheliograms obtained in the strong chromospheric lines. An early account of the weaker Unes was given by d’Azam-buja. McMath, Mohler, Pierce and Goldberg attributed intensity increases in (or decreases in depth of) metallic spectral lines to local temperature increases. Sheeley used high-resolution spectra to study these line weakenings further, finding them where, and only where, strong non-spot magnetic fields occurred. He also reported that in many cases the continuum in such regions was of reduced intensity, suggesting that fields often occur in the dark lanes and pores in the granulation. Spectroheliograms obtained in the cores of the weakened lines (e.g., Fel 6302.5Å) by Chapman and Sheeley showed that the bright network which these weakenings form appears as a sequence of sharp, bright points in the cores of the fainter lines and the wings of stronger lines but is more diffuse in the cores of stronger lines. They found the bright network in Zeeman-insensitive Unes (e.g., 5123.7A) also, indicating that it is due, at least in part, to variations in physical conditions. Lines of low ionization and excitation are weakened more than those of high ionization and excitation, and they attributed this to a temperature increase by 100-200 °K in the region of formation of the line cores ; a similar increase of 250 °K was found by Harvey and Livingston.

The first meaningful observation with the 80 MHz Cul-goora radioheliograph was made on 2 September 1967, a few weeks before the instrument was officially commissioned. Systematic observations, normally for 4 to 6 hours per day, began late in February 1968 and the Sun has since been observed on 438 days. The remaining days and many nights have been used for investigations of radio sources and the interplanetary medium and for maintenance and instrumental extension. The standard of reliability thus achieved has been due to the sustained efforts of K. V. Sheridan, W. J. Payten, K. R. McAlister, M. Beard and their colleagues. These first two years have been a period mainly of exploration—a phase of great interest to those engaged in observing, though possibly bewildering to those not. The present review is a first attempt to collate and summarize what has so far been found and where possible to draw preliminary conclusions. The observations to be described and their discussion have been due to a joint effort on the part of a number of workers, particularly G. A. Dulk (on leave from the University of Colorado), K. Kai (on leave from the University of Tokyo), N. R. Labrum, D. J. McLean, A. C. Riddle, K. V. Sheridan, S. F. Smerd, R. T. Stewart, and the present writer. The period has also seen considerable development in the evolution of intricate computer programmes for analysing the data, particularly on the part of L. H. Heisler and D. J. McLean.

Observations were made on 1970 February 9 using the Culgoora magnetograph to study the configuration and evolution of magnetic fields in a solar active region with high time resolution. The region observed was located at N20 E25 at the beginning of the observations which commenced at February 8, 22h 59m U.T. and finished at February 9, 07h 24 m. The magnetic fields were observed in the light of Cal 6102.7Å. Over a wavelength range corresponding to an intensity from 1/8 to 1/2 of the way up from line centre to the continuum on the blue side of the Une there is no apparent change in the field configuration, and the observations were made at a wavelength corresponding to the mid-point of this range. Exposures were made approximately every two minutes, with occasional large time gaps for instrumental adjustments.

Since the advent of the 80 MHz radioheliograph, precise position and polarization measurements have become available on several moving type IV bursts. Two of the more puzzling characteristics of these bursts are : (1) they exhibit strong circular polarization in parts or all of the source region ; (2) after moving outward to as much as 3 R⊙ with relatively constant intensity, they rapidly fade away. In this paper we discuss the polarization and intensity of synchrotron radiation from mildly relativistic electrons and suggest betatron deceleration as a mechanism to explain the rapid fade-out of the moving type IV sources. The results are applied to two examples of moving type IV bursts.

Recent two-dimensional observations of the quiet sun at 80 MHz by Sheridan showed a persistent low-intensity source (radio enhancement) whose daily motion was consistent with a source at radius 0.95 R® rotating with a synodic period of 27.3 d. In this paper we shall attempt to interpret this result in terms of the effects of refraction and opacity in model coronas. Comprehensive studies of the Sun at 169 MHz show that similar radio enhancements are associated with coronal streamers and that reasonable values for electron density and temperature within the coronal streamer allow the observations to be explained in terms of thermal radiation. Hence we shall consider only coronal models that possess streamer structure. We shall show that temperature enhancements within the streamer (‘thermal model’) do not lead to an apparent radius as small as that observed by Sheridan and that his observation may be better understood in terms of a non-thermal model for radiation from the streamer region.

A moving type IV radio source on 1970 March 21 was observed with the 80 MHz Culgoora radioheliograph to move out to a distance of p = 6 (where p = R/R®). Starting as a single source of complex shape it later developed strong circular polarization (> 90% R.H.) and separated into components which retained the same polarization. The source appeared soon after a prominence eruption (or flare spray) from which some of the ejected matter travelled in the same direction as, and with a velocity close to, that of the radio source.

The angular diameter of a star, combined with observed stellar fluxes in absolute units, allows the absolute fluxes emitted at the surface of the star to be calculated and thus provides a stringent test of model atmosphere predictions. Furthermore, if the flux distribution is observed at all wavelengths contributing significantly to the net flux, an empirical effective temperature can be found. Sufficient data are now available for Sirius (αCMa) to be studied in this way.

The theory of stellar convection zones has met three difficult problems. They are non-linearity, non-locality, and non-greyness of radiative transport. Non-linearity is inherent in turbulence. Non-locality is due to the nature of convection, that larger eddies are apt to be more unstable as indicated by the fourth-power dependence of the Rayleigh number on the vertical dimension. Inhomo-geneity and anisotropy of convection, penetration into stable layers, are the consequences. Non-grey radiative transfer through an eddy element is important in a convective atmosphere. In a preceding paper, the author has developed a theory which includes all these effects, using the representative eddy approximation. The emphasis in that paper was put rather in the non-locality and in the radiative non-greyness ; the treatment of non-linearity has been considered mainly in much earlier investigations. In the present note, we shall study how the representative eddy approximation is reconciled with the spectral theory of turbulence, and we shall determine the effective Reynolds and Péclet numbers, the coupling constants appearing in the eddy transport coefficients.

In an IAU Symposium report, Spiegel has made mention of the basic reasons for the astrophysical interest in the problem of non-linear convection of a horizontal fluid layer heated from below. Unfortunately the two important parameters of this problem—the Prandtl number P and the Rayleigh number R take on ‘extreme’ values in the astrophysical situation and this presents immediate difficulties as far as the numerical solution of the basic equations go.

The numerical solution of the basic equations for non-linear steady convection in the weak-coupling approximation is exceedingly difficult. In astronomical applications the Rayleigh number R will be of the order of1012, and we wish to report here some results obtained in the case of high Rayleigh numbers with the use of an asymptotic method.

The purpose of this paper is to obtain an expression for the reflecting properties of a semi-infinite, plane parallel, isothermal atmosphere of scattering factor λ. The absorption and scattering of the incident radiation is assumed to be entirely due to transitions in two-level atoms, and the absorption and emission profiles are given by <f>(y), y being frequency from line centre in Doppler units.

We consider the effect of a velocity gradient on the source function for a spectral line formed in an atmosphere in non local thermodynamic equilibrium, a problem examined previously by Kulander and Hummer and Rybicki. A numerical method is used which extends the Feautrier technique.

There exists a large number of varying methods of solution in radiative transfer theory. House and Avery have recendy published an exposition of the Monte-Carlo technique and the very nature of this solution makes it readily amenable, in theory, to the study of any transfer problem. Grant and Hunt have developed a method involving the invariant Sn matrix transformation and this also appears quite general in its application. Further, the Riccati transformation technique, developed by Rybicki and Hummer, has already been used in solving several different transfer problems. However, these methods have certain disadvantages. The equations are of first order and thus stability difficulties arise. Also, the finer details of the method rely, to a large extent, on the particular problem under consideration, and experience with such a method is required for the efficient computation of solutions.

An attempt is made to deduce the form taken by the distribution law for radiative scattering events performed by an atom whose energy—level structure is perturbed under conditions appropriate to the quasi-static limit.

A redistribution function R(x, x′)dx dx′ is defined as the probability that a photon with frequency between x and x + dx will be absorbed by an elemental atmosphere which then emits another photon the frequency of which lies in the range from x′ to x′ + ax′. The frequencies x and x′ are measured from the central frequency νo of the spectral line in units of the Doppler width Δ The particular functional form taken by R(x, x′) in this discussion will be given by

where α represents the broadening of the spectral line in units of the Doppler width while the function H(o, z) is defined by

the Voigt function. The function defined by means of equation (1) is one of that class of redistribution functions which combines natural and Doppler broadening. Therefore, it should be expected that any results obtained using this particular redistribution function will exhibit certain features characteristic of this type of scattering.