The domain of this symposium is so wide – essentially anything at all having to do with stars – that it is impossible to do more than cursory justice to even a small portion of the matters to be discussed. My contribution will therefore be limited primarily to a discussion of the status of theoretical work bearing on the behavior of stars that evolve through the classical instability strip that extends from the region of Cepheids to the domain of RR Lyrae stars. Discussion of other extremely important variable stars such as cataclysmic variables, Mira and irregular variables, flare stars, β-Canis Majoris stars, and δ-Scuti and small amplitude variables will here be mentioned only in passing; presumably, most of these stars will be discussed at length by other speakers at this symposium. Further little attention will be paid to the thermal instability that is initiated in the helium-burning region of a double-shell-source star and to current thinking about the progenitors of type I and type II supernovae; presumably, these topics will be discussed in Warsaw in the symposium on advanced stages of evolution.

The domain in the (U, V) plane of old-disk-population stars is defined by a sample of F- and G-type stars brighter than visual magnitude 6.5 for which luminosities are available from intermediate-band photometry. The majority of these old-disk stars avoid the domain of the young-disk population in the (U, V) plane except for (1) several objects with V near − 17 km s–1 and (2) a half dozen possible members of a solar group. The sample of stars used to define the old-disk population is confined to distances less than 100 parsec from the Sun and those with V near − 17 km s–1 may represent several generations of the objects formed in what is now the solar neighbourhood and which keep returning to this neighbourhood because they are isoperiodic (V near − 17 km s–1) with the local standard of rest. The half dozen possible members of a solar group indicate an evolutionary age of some 5 × 109 yr. In addition to some of the previously recognized stellar groups in the old-disk population (e.g. Wolf 630 and ζ Her), a new group with U = +40 to 50 km s–1 and V = −36 km s–1 is also discussed. The sample of red giants: (VE≤5m.0 and (R–I)0 > + 0m.42) contains eight probable members of the halo population of which five are members of the Arcturus group. Possible structure in the old-disk-population giant sequence is discussed on the basis of published narrow-band indices, and the luminosity functions of the old- and the young-disk-population red giants are compared.

Most of the material presented can be found in Eggen, O. J.: 1973, Publ. Astron. Soc. Pacific85, 542.

This review consists of a discussion about the agreement of non-linear calculations at very low amplitude with linear theory results, the recent computational advances in progress, the current problems especially those relating to observations, a review of current computations, and finally the presentation of some recent extensive non-linear calculations.

The quantitative discrepancies between theory and observation with regard to population I Cepheids are discussed. The discrepancies cannot be reconciled by mass loss or by changes in the luminosity or effective temperature of the variables. It is concluded that the present pulsation models both linear and non-linear are in error.

In the study of Cepheid pulsation and evolution, it is very important to be able to obtain effective temperatures from some easily observable spectral characteristic. A review is given of the several discrepant relations between Teff and intrinsicB—V index given for classical Cepheids and/or yellow supergiants by Rodgers (1970) and Parsons (1971) (the same as Kraft, 1961; Böhm-Vitense, 1972; Schmidt, 1972, and van Paradijs, 1973). All temperatures agree well at (B – V)0 = 0.4 but diverge toward redder colors; at (B – V)0 = 0.9 the values range from 4900° (Böhm-Vitense, for class Ia-Ib) to 5770° (Schmidt, for class I stars). In each case the analysis leading to the assignment of Teff to a given color index is not completely satisfactory, so it is difficult to make value judgements. Comparison of relations between Teff and spectral class shows similar discrepancies.

Synthetic stellar spectra have been computed for Cepheids and supergiant F and G stars, using flux constant model atmospheres. These spectra have been used to compute theoretical uvby and UBV colours which may be compared with the observed colours. The supergiant α Per is used to establish the zero points of the theoretical colours. The colour comparison can be used to determine the temperatures, gravities and metal abundances of the stars as well as an estimate of the interstellar reddening. The reddening determinations are carried out by arguing that the temperature and gravity values obtained from U – B and B – V must match those obtained from c1 and b – y.

A more detailed account of this work will be given elsewhere.

With specially computed detailed tables of equations of state and opacities, the instability strips for δ Scuti stars and Cepheids of population I and RR Lyrae and W Virginis stars of population II have been compared using the linear pulsation theory. Uncertainties in the observed strip locations and sometimes the mode of the observed pulsations do not allow high accuracy in fixing helium contents or the variables masses. Nevertheless, if masses close to those given by evolutionary theory are used, the helium content in population II objects is likely less than Y = 0.25. A helium content of close to zero would put the theoretical blue edge of the instability strip to the red of the observed red edge, and have all the hotter stars which are in the strip as non-pulsating. For population I, Y can be more than 0.3, (more than 0.4 if half evolutionary masses are used), but if a given star has Y less than about 0.2 (full mass) or 0.25 (half mass), it can appear in the dwarf and classical Cepheid strips as non-pulsating.

Due to recent contradictory results, the period-luminosity-color relation of δ Scuti stars has been examined by a maximum likelihood method. δ Scuti stars are found to definitely obey a period-luminosity-color relation. The derived coefficients are very similar to those derived for RR Lyrae variables. Care has to be taken to allow for the large mass differences between the population I variables, such as δ Scuti stars, and population II ultrashort period pulsators.

A comparative investigation of the temperatures, gravities and abundances of the AI Velorum stars and some selected δ Scuti stars and RR Lyrae stars has been carried out at Mount Stromlo during the past few years. Eleven AI Velorum stars, 6 δ Scuti and 6 RR Lyrae stars together with 6 established standard stars have been observed. The eleven AI Velorum stars comprise almost all those accessible from the Southern Hemisphere. The RR Lyrae stars were selected as examples of the weakest and strongest line stars of type a and c, and the 6 δ Scuti stars observed also represent the strongest and weakest line stars of the group.

Intermediate-band photometry has been used to derive effective temperatures, metal abundances, and surface gravities of nine stars of the dwarf Cepheid group of variable stars. A strong correlation exists between the metal-line strengths and the period of pulsation in the sense that the shorter-period stars have weaker metal lines. The dwarf Cepheids are evidentally found among both population I and population II stars.

Four δ Scuti stars (θ Tuc, ϱ Phe, 1 Mon and 21 Mon) have been observed intensively in an effort to understand the periodicities present in these stars. The stars selected were known to be of variable amplitude and relatively large light range. The data of each star was Fourier analysed. In no case did the period ratios have values consistent with the period ratios of low order radial modes. The most interesting result appears in the analysis of 1 Mon. The three principal periodicities present occur at P1 = 0.13612, P2 = 0.13378 and P3 = 0.13855 days. To within the errors these periods form an equal frequency split, i.e. 1/P2 −1/P1 = 1/P1 −1/P3.

Recent publications have discussed the existence of stable B stars in the β CMa instability strip of the (β, Q) plane (Lesh and Aizenman, 1973) and the (log g, θe) and (Mbol, log Te) planes (Watson, 1972). The new lists of Strömgren uvbyβ photometry published by Crawford et al. (1970, 1971a, 1971b) for most of the B stars in the Bright Star Catalogue suggested that one might determine quite precisely the proportion of stable B stars (that is, stars not known as β CMa variables) in a luminosity/colour plot in the form of the β index against [c1] = c1 −0.2 (b – y).

Following Davey (1973), we have considered the linear radial pulsational stability of stellar models in the region of the HR diagram populated by β Cephei stars. Instead of one composition, however, we have considered many compositions, some of them rather extreme. No consideration of composition changes for temperatures above a few-million degrees was given, and therefore the stellar structure and its pulsational stability may not be evaluated very accurately. Modulation of nuclear reactions was also neglected. In no case was radial pulsational instability found.

Massive main sequence stars are vibrationally unstable to small perturbations excited in the region of nuclear energy generation. This instability may, however, be limited at finite amplitude. Only the fundamental radial mode is unstable with an e-folding time of 105 to 106 pulsation periods; in contrast the overtones have damping times short compared with the growth time of the fundamental. Non-linear effects couple the linear modes. At very low amplitude the energy transfer time between modes is long compared with both growth and damping times and, as the overtones decay, a pure fundamental should result. However, as the amplitude increases, the transfer time becomes less than the growth and damping times. Energy can then be transferred from the fundamental to the overtones and damping can lead to a limitation of amplitude.

The variability of the B–G supergiants is studied here with a set of 500 observations made for 76 stars. In addition to the discussion on the variability in colour indices (Maeder and Rufener, 1972), we also include the analysis of the apparent magnitudes. The observations, made randomly in time over several years, are selected from the new Catalogue (Rufener, 1974) of stars measured in the Geneva Observatory system. Some results on the luminosity dependence of the variations are presented in Table I.

The objective prism surveys carried out by Sanduleak (1968, 1969) make available for the first time a relatively complete and homogeneous list of the brightest stars in both Magellanic Clouds for the range of spectral types O–G5. Photometric observations in the four color, Hβ system of the 169 candidates in the SMC and the 45 brightest stars in the LMC as well as spectroscopic observations of the most luminous early-type stars, lead to the following picture of the stability and evolution of very massive stars:

1. (1) The reddening is the same for the most luminous stars in both Clouds and there is a sharply defined upper limit to the stellar luminosity, which is also the same in both Clouds. This limit corresponds to Mbol = −11 ± 1 or 90 in good agreement with the classic study of Feast et al. (1960).

2. (2) The stars of highest total luminosity are the blue supergiants, and in both Clouds the high temperature limit corresponds to type B1.5 or Te ~ 25000 K for Mv ~ −8. The SMC appears to be deficient in luminous F5–G5 supergiants.

3. (3) With few exceptions the most luminous stars are not known to show more than low amplitude variations in light. They do show Hβ emission as expected, and four stars in the LMC have anomalously strong emission, indicative of unusual atmospheric activity. Bright Wolf-Rayet stars have long been known in the Clouds; in addition, several candidate Of stars are indicated by the photometry.

4. (4) The brightest B-type supergiants in the SMC appear to be deficient in N, Si, O, and probably Mg and C, although helium is normal, a result worth pursuing in the less luminous stars.

5. (5) Judging from the numbers of the brightest stars, the recent rate of star formation in both galaxies per unit mass is quite similar despite the fact that the SMC has a larger fraction of neutral hydrogen and the LMC a more conspicuous display of Hii regions.

Attention is drawn to a group of stars of luminosity class Ia, in which variation of radial velocity has long been known in semi-regular cycles of 5 to 30 days. The interval of approximate repetition appears to be positively correlated with the luminosity of the star.

Recent spectrophotometry of the absorption lines, especially by Rosendhal, Aydin, Groth, and Buscombe shows a considerable variation in the strength of Balmer lines (with emission components detected at H∝), as well as those of metallic ions. The microturbulence parameter derived from curves of growth for Fe ii varies by a factor of two or more during some cycles.

This paper discusses the following topics: (1) Mira Variables in Globular Clusters; (2) infrared observations of Globular Cluster Variables; (3) carbon Stars in Magellanic Cloud Clusters; (4) the Se Variables and the superlithium rich Variables.