It is now nearly fifty years since Eddington and Milne had a lively controversy on the importance of the surface boundary condition on the internal structure of stars [see Eddington (1930) and Milne (1930)]. We remember that Eddington believed that the internal structure of stars is basically determined by the physical processes occurring in the deep interior and that what happens in the surface layers has little effect on the total stellar luminosity. On the other hand, Milne emphasized the importance of the properties of the outer layers and the effect these could have on the run of pressure and temperature in the deep interior of the stars. We know now that both Eddington and Milne were correct. Eddington’s considerations apply to the hot stars, the early-type stars which have surface layers in radiative equilibrium. Milne’s arguments are relevant to the cool stars, the late-type stars which have deep convective envelopes. In the former case, one can safely assume in calculations of stellar structure that the density and the temperature both approach zero simultaneously at the surface (the so-called “zero” surface boundary conditions).

I begin by stating very explicitly and unambiguously that I completely disagree with any idea that a stellar atmosphere can be in any sense a boundary of the star, or that the atmosphere sets boundary conditions on stellar structure. Such an idea is what underlies all the single-layer, LTE atmospheric models, which misdirected atmospheric studies for so many years by introducing a false separation between “normal” and “extended” atmospheric phenomena. On the contrary, I assert that a more correct physical picture for the atmosphere than as a boundary comes from the characterization of star and atmosphere as:

(1) The STAR is: a concentration of matter and energy, C (M, E), in its parental environment, the interstellar medium (ISM); with boundary conditions on stellar structure being set by the way one models (a) storage modes for matter and energy in the star and ISM, and (b) energy generation in the star.

Some 30 years ago it became clear that the solar corona is a plasma with a temperature of the order of 106K. As the underlying layers have only temperatures of 5000 K a mechanism had to be discovered, capable to explain this high temperature. A solution to the problem was found when it was realized that mechanical energy losses, by shock dissipation of wave energy can heat up a plasma to such high temperatures. This mechanical energy is formed in the deeper layers of the atmosphere and transported outwards. Dissipation becomes significant in regions where the density is sufficiently low.

Wave propagation in a compressible medium in the presence of gravity and magnetic fields has been treated as a general problem, among others by Ferraro and Plumpton [1958). Three basic parameters are present: compressibility of the medium, gravity and magnetic field.

A brief summary of the current status of radiatively driven wind models for early-type stars is given. A critique of these models is made both on theoretical and observational grounds, and it is concluded that a pure radiatively driven wind is probably not a realistic approximation for 0-star winds. It is argued that probably the wind structure must have an initial high-temperature (“coronal”) region through which the trans-sonic flow takes place, followed by radiative accelerations to very high terminal velocities. Full details of the discussion can be found in Stellar Atmospheres, 2nd Edition, by D. Mihalas, to be published by W. H. Freeman and Company, San Francisco, in Fall 1977.

In the absence of turbulence or convection one expects that, in stars, heavy elements would tend to settle gravitationally while light elements would go to the surface. Eddington (1930) however realized that this general tendency could be modified both by the electric field and by differential radiation pressure. In spite of their small mass, electrons do not all float on the surface of stars because an electric field is generated that keeps them from separating from the protons. Instead of settling gravitationally, heavy elements often concentrate on the surface because they absorb relatively much more photons than hydrogen or helium and are dragged to the surface by the radiative flux. Eddington concluded that turbulence was too strong for diffusion to be important in stars since the relation that diffusion predicts between surface abundances and stellar masses did not appear to be realized in most stars.

Since the work of Michaud (1970), the abundance anomalies observed in the peculiar Ap and Am stars are increasingly believed to be a consequence of diffusion processes in stellar atmospheres or stellar envelopes. A number of the problems that seemed at first sight insoluble within the framework of diffusion processes have now been solved by it. Diffusion processes can, for example, account for anonalous helium isotopic ratios (Vauclair et al, 1974 (b)) and mercury isotopic ratios (Michaud et al, 1974). Quantitative results on abundance variations due to diffusion processes have been obtained (Michaud et al, 1976; Michaud, this conference; Alecian, 1976). They show that, in general, the relative abundance anomalies obtained from computation are close to the observed ones. It is now well established that the largest abundance anomalies observed in Ap stars (for rare earths) can be interpreted by diffusion processes with a satisfactory time scale, in a completely stable atmosphere. However, the predicted absolute abundance variations often exceed the observed ones, as in the case of Am stars. This suggests that the assumption of stability is not completely valid for the stellar gas: some kind of macroscopic motion, such as a meridional circulation or turbulence or both, must be at work and slow down the diffusion.

Dr. Pagel has given us a fine summary of the observations relevant to the topic I am to cover. Drs. Michaud and Vauclair have described in detail the potential effects of diffusive processes which might well explain, at least in part, the apparent abundance anomalies observed in the peculiar A stars and the magnetic A stars. In the paper following mine, Dr. Boesgaard will present the observational evidence regarding the abundance of the light elements lithium, beryllium and boron, and relate these observations to the theory of stellar envelopes. With these important topics expertly covered I shall restrict myself to the single question: How do some reasonably common types of stars, such as the carbon stars and the S stars, manage to show off at their surfaces, for us to observe, a fair sampling of the products of the nuclear burning going on deep in their cores?

I should like to confine this discussion of the decay of the light elements to Li, Be, and B since the observations of D and He in stars are not relevant to the decay in stellar envelopes. The light elements are trace constituents best observed in the resonance lines. Only Li I and Be II have resonance lines which can be studied from ground-based observations. Therefore we know the most about abundances in stars where these ions can be observed and how those abundances are affected by stellar evolution. I will first discuss the cosmic or initial abundances of Li, Be, and B to establish the “zero-point” from which the decay occurs. Then observations and interpretations relevant to the decay and to stellar evolution will be considered.

This joint discussion has amply demonstrated that stellar atmospheres are not passive and dumb bodies just sitting there at the surface of a star.

First of all the surface “feel” fundamental parameters of the star as a whole, specifically the ratio L/R2 and m/R2. As these fundamental parameters are affected by stellar evolution, the surface layers reflect to a large extent the degree of evolution of the star. This is the main basis for photometric and spectral classification systems. One could even claim that the observation of the stellar atmosphere would univocally determine the state of evolution of the star if i) it was always possible to determine the atmospheric abundances of the key elements to internal structure and ii) if the chemical composition of the atmosphere was always representative of the chemical composition of the whole star. Unfortunately a serious problem occurs for i) with the abundance of helium which element has no photospheric absorption line for all spectral types later than B and also with ii) in a more limited portion of the HR diagram, mainly in late B and A slow rotators. But whereas point i) is a mere problem of contingency, point ii) is a basic problem, greatly overlooked in the past, and to which one fourth of the joint discussion was devoted.

If the Sun is observed like a star, without spatial resolution, its magnetic field seldom exceeds 1 Gauss. But with high spatial resolution the field is seen to be largely concentrated into kG structures. Observations of the structure and dynamics of solar magnetic fields can therefore provide a guide to the nature of magnetic fields of other stars which cannot be resolved. Solar activity and the structure of the chromosphere and inner corona are intimately linked with magnetism and a complete understanding of these features often depends on magnetic field details. There are unsolved physical problems involving solar magnetic fields which have challenged many physicists. For example, confinement of small-scale fields in kG structures is a problem of current interest (Parker, 1976; Piddington, 1976; Spruit, 1976). Solar observers are no less challenged since the Sun presents us with a complicated magnetic field having a range of scales from global to less than the scale of our best observations as illustrated in Figures 1, 2, and 3. This paper is a survey of observational techniques and results at the small-scale end of the spectrum of sizes in the solar photosphere. This topic has been frequently reviewed (e.g. Athay, 1976; Beckers, 1976; Deubner, 1975; Howard, 1972; Mullan, 1974; Severny, 1972; Stenflo, 1975) so that recent work is emphasized here.

One of the most exciting developments in solar physics over the past eight years has been the success of ground based observers in resolving features with a scale smaller than the solar granulation. In particular, they have demonstrated the existence of intense magnetic fields, with strengths of up to about 1600G. Harvey (1976) has just given an excellent summary of these results.

In solar physics, theory generally follows observations. Inter-granular magnetic fields had indeed been expected but their magnitude came as a surprise. Some problems have been discussed in previous reviews (Schmidt, 1968, 1974; Weiss, 1969; Parker, 1976d; Stenflo, 1976) and the new observations have stimulated a flurry of theoretical papers. This review will be limited to the principal problems raised by these filamentary magnetic fields. I shall discuss the interaction of magnetic fields with convection in the sun and attempt to answer such questions as: what is the nature of the equilibrium in a flux tube? how are the fields contained? what determines their stability? how are such strong fields formed and maintained? and what limits the maximum field strength?

Since Dr. Harvey has already mentioned the main results of my observations, I want to restrict myself to two topics:

1. i) a brief description of the improvements of my method as compared to that used by Stenflo (1973),

2. ii) some puzzeling aspects of my results which might be discussed in this meeting.

The main differences between the two methods of simultaneous Zeeman polarization measurements used by Stenflo (1973) and by myself are based on suggestions by Schröter (1973):

1. a) use of three instead of only two differently split lines;

2. b) use of less temperature sensitive lines;

3. c) use of model atmospheres instead of a Milne-Eddington model for the calculation of the ‘calibration curves’;

4. d) observation of selected Ca+K features in order to avoid the statistical method with the scatter-plot diagram.

Historically, attempts to model the temperature structure of faculae have generally suffered from a rather basic contradiction. Models which were based on center to limb measurements of the continuum contrast of faculae disagree with models that are based on measurements of line profiles in faculae. The “continuum” models predict line weakenings which are of larger amplitude than what is observed, and the “line profile” models predict a continuum contrast that is less than what is observed. Chapman (1976) discusses this problem in some detail. It is the purpose of this paper to show that there is a fundamental reason for this historical contradiction between line profile measurements and continuum contrast measurements: The line profile and the continuum contrast of a given facular are both a function (the two functions are different) of the size of that facula. The first indication of this fact was given by Frazier (1971). Figure 1 shows the contrast of faculae in the core of the line Fe Iλ 525. 0 nm, and in the continuum, as a function of the observed magnetic flux. One can see immediately that the contrast in each channel depends on φ in a much different manner. Therefore, one can conclude that the shape of the entire line profile will vary as a function of φ. On the basis of Figure 1, we must expect that this variation of the line profile will be continuous from infinitesimally small faculae up through very large faculae, and indeed, all the way up to pores.

Photospheric faculae are now believed to be closely associated with the small-scale solar magnetic field. In order to obtain reliable observations of solar magnetic fields, one needs to have a good description of faculae, which is presently lacking. The problem in obtaining good observational data is severe because faculae are usually not spatially resolved, particularly so in the case of spectroscopic observations. Proper use of spectroscopic observations also requires some knowledge of solar velocity fields and atomic physics in the case of a non LTE analysis. Many of these problems can be avoided by making use of the wings of the Ca II K-line. The wing of this line is unaffected by magnetic and velocity effects. The formation of the line has become increasingly well understood and most of the wing (with the exception of the inner 1 - 2 Å) is formed in LTE. The line is so strong that its formation spans the whole depth of the photosphere.

In an attempt to interpret the observed properties of small scale magnetic fields at the solar surface, a set of models has been calculated based on the assumption of a magnetostatic equilibrium. The basic assumptions made are:

1. i. The observed magnetic elements are magnetostatic flux tubes.

2. ii. The efficiency of convective heat transport inside the tube is reduced with respect to that in the normal convection zone; the horizontal convective heat transport in the tube is suppressed completely by the magnetic field.

3. iii. Close to the tube, horizontal convective heat transport is reduced due to the proximity of the magnetic field.

Harvey has reported in this discussion observations of mean downflows in magnetic elements that increase in speed with depth. It is therefore pertinent to ask what role such flows may play in the production and maintainance of the flux concentrations.

Equilibrium Models

The first thing to be said is that such flows cannot directly influence the horizontal momentum balance, i.e. their dynamic pressure is negligible.

A steady internal flow such as that proposed by Ribes and Unno (1975) for chromospheric concentration would require supersonic flows with very large curvature at photospheric levels. There is no evidence for transverse flows of such magnitude.

Recent interest in the subject of this discussion gained momentum by an observation which did not concern magnetic fields directly. The filigree which Dr. Richard Dunn on Sacramento Peak found 2 Angstrom off the center of Hαis a bright and crisp structure in the photosphere with a width o: 1/5 arcsec. It was described in proper detail by Dunn and Zirker (1973). Even in the printed pictures in their paper one clearly sees one step beyond the solar granulation. The filigree is certainly related to the small scale structure of the photospheric magnetic field, but it is not yet clear whether the flux elements are exactly cospatial and have the same small dimensions. Simon and Zirker (1974) concluded froi spectra that the field structure is wider than the filigree. On the other hand Harvey (1976) in his excellent review of the observations has also presented the arguments of several authors who conclude that the sizes of the flux elements are as small as those of the filigree. This discrepancy certainly needs further study before such even more delicate questions as the spatial extent of the downdraft inside and around the flux elements can be reliably answered from observations. The theoretical interpretation of the downdraft depends on this answer as different sources of the mass flow are involved: the overlying atmosphere and the convergent mass flow of the surrounding convection. The latter stays partly outside the flux element, partly diffuses into it with an efficiency that might be enhanced by convection of still smaller scale.