It is a great privilege to have the opportunity to welcome William Morgan to the IAU Symposium that has been opened today.

The basic equations for constructing a stellar atmosphere (hydrostatic equilibrium, flux constancy, radiative transfer, convective instability) are briefly summarized. While the parameters Teff (effective temperature) and g (surface gravity) are directly contained in these equations, the element abundances ∈i enter only indirectly through the thermodynamic properties (such as electron pressure, entropy, …) and the absorption and scattering coefficients of stellar matter.

The equation of state, convection, the effects of the absorption coefficients (particularly of line absorption) on the temperature stratification, and the role of velocity fields (microturbulence) are discussed in some detail, emphasizing their dependence on the abundances.

From a given model atmosphere, a ‘theoretical spectrum’ (colours, bolometric correction, line strengths etc.) can be calculated. The (relative) fluxes emerging at the surface are essentially determined by the temperature gradient and the absorption coefficients at the frequencies under consideration. The basic goal of quantitative classification, however, is the inverse problem, namely to deduce the stellar parameters from selected observed spectral criteria. Aspects relevant to this problem such as the question of uniqueness and the occurrence of possible systematic errors (even when using differential analysis techniques) are briefly sketched and illustrated by some examples.

The ATLAS programme has been corrected and modified for use at low effective temperatures. A grid of unblanketed model atmospheres has been generated for the region G5-K5, V-II. A spectrum synthesis programme has been written for the calculation of flux vs wavelength for selected regions of the spectrum. Temperature distributions from the grid of continuum models and from published blanketed models will be used along with published oscillator strengths as input data for the spectral synthesis programme.

Spectrograms of MK standards have been taken at 12 Å mm−1 and 120 Å mm−1. The University of Toronto PDS microdensitometer system has been programmed to allow comparison between the synthesized spectra and the observed spectra to determine the effects of effective temperature, surface gravity, microturbulence, and abundance on classification criteria.

We have analysed the spectrum of Arcturus (K2 III) relatively to the Sun, using a differential technique employing empirical models for both stars. We derive an effective temperature of 4260 ± 50K and a surface gravity log g = +0.90 ±0.35; these in turn lead to a very low mass, in the range 0.1 to 0.6 M⊙. Elements are found to be underabundant by an average factor of 4 compared with the Sun. The abundance patterns in the two stars are significantly different, in keeping with the belief that Arcturus is a star of an older generation than the Sun. The carbon isotope ratio, which is as small as 5 or 6, shows that the atmospheric material of Arcturus has been processed through the CNO cycle, and theoretical arguments also indicate that Arcturus is somewhat evolved.

In cool stars, the determination of abundances of elements requires the resolution of the chemical equilibrium for each element even if atomic lines only are used. In the past, several authors have solved the well-known system of equations for a limited number of elements and of molecules. New calculations have been performed with special emphasis on the completeness of the system. Thus, all stable elements (83) have been included and a lot of molecules have been selected in order to omit no abundant compound. Owing to the lack of data (since many molecules are as yet not known spectroscopically), it appeared necessary to estimate many molecular parameters. Approximate equilibrium constants have been determined from analogies found among known molecules.

It has been shown once more that the dissociation energy is by far the most important parameter, which yields alone the final accuracy.

Our calculations include about 1200 molecules, of which more than half are new compounds never introduced in earlier investigations. We have found that, for about twenty elements such as Ti, Zr, La and most of the lanthanides, the new molecules play an important role in the chemical equilibrium. The cases of titanium, zirconium and lanthanum have been particularly investigated owing to the use of several bands of their oxides in the spectral classification of M- and S-type stars. We have noted that the experimental determinations of the dissociation energy of most monoxides and dioxides are as yet rather inaccurate. Furthermore, neither the spectrum nor the heat of atomization of hydroxides are known in the laboratory. It has appeared that estimating the dissociation energy of hydroxides was particularly difficult in consequence of the lack of data for such molecular compounds.

For oxygen-rich stars, we have investigated the influence of uncertainties of the dissociation energy of the most abundant species on the march of the molecular concentrations. In the case of titanium, we have found that the concentration of TiO strongly changes at low temperature (T <2520 K) according to the adopted Doo- values for TiO, TiOH and TiO2. Therefore, the interpretation of the TiO bands in the coolest stars has to take this new effect into account. In any way, we have checked that the TiO concentration always increases from early K- to late M-type stars. We have also shown that the depletion factor for Ti presents a final uncertainty of a factor of about ten at 2520 K, which still increases at lower temperature. That is due to the cumulative effect of the inaccuracies of molecular data. Therefore, in late M-type stars, the determination of the abundance of titanium remains rather uncertain even if it is derived from Ti I or Ti II lines. The present inaccuracy will only be reduced from very precise measurements of the dissociation energy of the relevant molecules. For Zr and La, we have found similar results to that for Ti. Furthermore, we have noted that there is no determination of absolute transition probabilities for the ZrO and LaO bands (contrary to TiO bands) which are both of first importance for the spectral classification of cool stars.

For carbon-rich stars as well as for S-type stars (i.e. O/C very near unity), we have checked that the molecules always play a much less important role that in oxygen-rich stars, as it was first noted by Tsuji (Astron. Astrophys.23, 411, 1973).

Our conclusion is that there is an urgent need of accurate measurements of the dissociation energy of many molecules and also of band oscillator strengths for most of the transitions of stellar interest. Furthermore, several new selected compounds have to be investigated in the laboratory, especially the dioxides and hydroxides. Such accurate molecular data are necessary in order to get a better knowledge of the physical conditions in cool stellar atmospheres.

The Eggen-Greenstein (1965) classification of cool white dwarfs (DC, DF, DG, λ 4670, λ 4135) was based on the features visible in the spectra of low dispersion. Detailed model atmosphere computations (11000 ≥ Teff ≥ 7000 K) and comparison with spectra observed by Wegner (1974, 1975) show that the variety of the spectra is due to changes in the abundance ratios of C/O, C/H and H/He only. Thus the relative strengths of the C2 and CH-bands can be used for classification and guess of Teff in the range of Teff ≥ 6000 K.

In order to study the atmospheres of cool white dwarfs of spectral types DA, DF and DG, model atmospheres have been calculated for temperatures 5000 ≤ Teff ≤ 7000 K and gravities 7 ≤ log g ≤ 8.5. The helium to hydrogen abundance ratio ranges from 0.1 to 1000. The abundances of the metals ∈M (relative to hydrogen) vary between the solar value ∈⊙M and ∈⊙M/1000. The models are hydrogen and metal line blanketed and in radiative equilibrium. The models with increased He abundance are characterized by a decreased mean opacity since the absorption cross-section of He is much smaller than that of H–. As a result, the spectral lines become stronger and – due to the much higher pressures – much broader. A reduction of the metal contents also increases the pressures. In this case it is caused by the shortage of electron suppliers. Here the spectral lines also become broader, but in general weaker.

These effects strengthen the overlap of the lines due to the high gravity of white dwarfs and more or less lead to a quasi-continuum which may be much below the true continuum. Because of the wavelength dependence of the line density the depression is strongest in the UV and blue spectral region, whereas for wavelengths λ ≥ 4500 Å the difference from the true continuum is only a few per cent. The details will be published elsewhere.

A few examples are given showing the utility of the catalogue of iron/hydrogen determinations for astrophysical researches. These are:

1. (a) Histograms of dwarfs and giants analyzed in detail with spectral type between O and M.

2. (b) Logarithmic abundances diagrams of given stars.

3. (c) The impact on spectral classification of high-dispersion-detailed-analysis results.

4. (d) The use of well-determined chemical and physical parameters of nearby stars for the construction of HR diagrams in the (Mbol –log Teff) plane.

The spectra of F, G and K stars having the iron lines at their best visibility, special emphasis has been given to the results concerning these stars.

Several points of detail which affect stellar abundance determinations are discussed. In particular, the importance of including the effects of hyperfine structure and isotopic shifts when considering the lines of some elements is stressed.

The abundance determinations for F dwarfs by Bell and Peytremann, who use theoretical calibrations for intermediate band photometry, and Nissen, who observes very narrow spectral intervals, are intercompared. The agreement between Bell and Nissen, who have 46 stars in common, is quite satisfactory.

Recent work on carbon and nitrogen abundances in cool stars is described. The suggestion of Hearnshaw, that [C/H] = 1.5 [Fe/H] for disc stars with −0.7 < [Fe/H] < 0.4, is compared with recent results by Clegg. Whilst Clegg's results are quite precise, they neither confirm nor deny Hearnshaw's suggestion. Work by Branch and Bell on K giants shows that [C/Fe] = 0, or a constant, for the stars in the sample. A value of about 7 for the C12/C13 ratio in the atmosphere of Arcturus has now been confirmed by several authors and Lambert and his collaborators have determined this ratio for several K giants.

The suggestion by Spinrad, Taylor and others that the M67 dwarfs are more metal-rich than the Hyades, i.e. that they are super-metal-rich or SMR, seems to be erroneous. However some SMR stars, such as 31 Aql, certainly exist even though there is still some uncertainty in the precise abundance of strong CN stars such as μ Leo.

Examples of synthetic spectra for metal-deficient giant stars are given and a theoretical colour-colour diagram is compared with observations of globular cluster and Draco stars.

The abundance effects on the tri-dimensional representation for the A0-G2 stars in the Geneva system are reviewed. B2–V1 and d are not affected by the Am characteristic, but B2–V1 is too blue (blocking effect on V1) and d smaller for the Ap stars. For B2–V1 ≥ 0.230, we have a residual effect Δ(B2–V1) = 1.20 (Δm∗2 + 0.060). d is also affected and the residual effect is Δd = −0.4 Δm2 for Δm2 ≥ −0.060 and Δd = −1.1 Δ(B2–V1) −0.024 for Δm2 < −0.060.

The abundance effects on the relations between B2–V1 and the parameters of temperature in other systems are studied.

Abundance differences from one star to another cause differences in the observed parameters of the Strömgren four-colour system. The major effect is on the m1 parameter, of course.

This paper describes these effects on the parameters.

A test has been made of the reliability of the multidimensional classification of late-type stars from low dispersion objective prism plates recently attempted by Stock and Wroblewski. Such classification at low dispersion is difficult due to the problem of separating the effects of luminosity from those of abnormal metal abundance. A sample of the stars classified by Stock and Wroblewski as metal weak (pec) and of those classified as luminous stars (class I) were observed using the DDO intermediate-band system. The photometry shows that the stars classified as pec are indeed population II giants, of low metal abundance ([Fe/H] < −1.0). The stars classified as I, however, were found in general not to be true supergiants but rather a mixture of various types of giants, such as CN strong stars, with spectral features that resemble, in one way or another, those of higher luminosity stars.

The Geneva photometric system has been calibrated in terms of [M/H], θeff, Mv in the spectral range F5 to K4. As the spectral type is a datum generally available, we derive empirical relations showing the coupling of θeff and [M/H] at given spectral type and luminosity class. Similar relations are offered for the absolute magnitudes and provide a more accurate means for deriving spectroscopic parallaxes. Systematic effects on the estimation of the luminosity class are also shown.

The α and λ photometric systems are used to obtain a bi-dimensional representation of the A and F stars.

A photoelectric narrow-band index, I(4026), of the He I λ 4026 line has been observed with an echelle spectrometer for B-type stars in young clusters and associations.

Model-atmosphere computations of the Strömgren [c1] index, the Hβ index, and I(4026) as functions of Teff, g and the helium-to-hydrogen ratio have been used to derive these atmospheric parameters from the observed indices for each star.

For the OriOBIb, LacOBI and Sco-Cen associations 11 out of 48 stars in the temperature range from 14 000 to 20 000 K are found to be helium poor in the sense that the derived helium-to-hydrogen ratios lie in the range from 0.05 down to very low values. In the temperature range from 20 000 to 30 000 K no helium poor stars are found, but two stars in OriOBIb are helium rich. Both of these stars show rather strong variations of the I(4026) index.

All stars in h + χ Per and CepOBIII are apparently helium deficient compared to nearby field stars.

The term helium-rich stars here refers to those stars with apparent spectral types near B2 ana helium lines which are enhanced, but not stronger than the hydrogen lines. The previously known helium-rich star HD 184927 has been found to be a spectrum variable; the equivalent widths of the helium lines changed by an average of 46% between two observations. HD 186205 has been newly recognized as a member of the helium-rich class. Further work toward understanding the rapidly variable Ha emission in the prototype helium-rich star, Sigma Orionis E, is in progress in co-operation with Dr J. E. Hesser at CTIO.