“If simple perfect laws uniquely rule the universe, should not pure thought be capable of uncovering this perfect set of laws without having to lean on the crutches of tediously assembled observations? True, the laws to be discovered may be perfect, but the human brain is not. Left on its own, it is prone to stray, as many past examples sadly prove. In fact, we have missed few chances to err until new data freshly gleaned from nature set us right again for the next steps. Thus pillars rather than crutches are the observations on which we base our theories; and for the theory of stellar evolution these pillars must be there before we can get far on the right track.”

The place of stellar physics in Astrophysics is not the same as it were 50 years ago. Stellar evolution theory has been one of the preferred places of numerical calculations, and as a consequence, standard evolution models, from the homogeneous pre-main sequence star to the final stages, white dwarfs, neutron stars, supernovae, has become sort of archetype of numerical analysis and computation, the essence of perfection.

Carbon stars are thought to be in the asymptotic giant branch (AGB) phase of evolution, alternately burning hydrogen and helium in shells above an electron-degenerate carbon-oxygen (CO) core. The excess of carbon relative to oxygen at the surfaces of these stars is thought to be due to convective dredge-up which occurs following a thermal pulse. During a thermal pulse, carbon and neutron-rich isotopes are made in a convective helium-burning zone. In model stars of large CO core mass, the source of neutrons for producing the neutron-rich isotopes is the 22Ne(α, n)25Mg reaction and the isotopes are produced in the solar system s-process distribution. In models of small core mass, the 13C(α, n) 16O reaction is thought to be responsible for the release of neutrons, and the resultant distribution of neutron-rich isotopes is expected to vary considerably from one star to the next, with the distribution in isolated instances possibly resembling the solar system distribution of r-process isotopes. After the dredge-up phase following each pulse, the 13C is made by the reactions 12C(p,γ) 13N(β+ v) 13C in a zone of large 12C abundance and small 1H abundance that has been established by semiconvective mixing during the dredge-up phase. There is qualitative accord between the properties of carbon stars in the Magellanic Clouds and properties of model stars, but considerably more theoretical work is required before a quantitative match is achieved.

The observed paucity of AGB stars more luminous than MBOL ∼ −6 is interpreted to mean that the AGB lifetime of a star more luminous than this is at least a factor of ten smaller than the AGB lifetime of stars less luminous than this, or, at most 105 yr. Since, with current estimates of the 22Ne(α, n)25Mg reaction rate R22, only AGB model stars more luminous than MBOL ∼ −6 can produce s-process isotopes in the solar system distribution, it is inferred that either (1) the current estimates of R22 are too small by one to two orders of magnitude, allowing less luminous AGB stars to contribute, (2) the solar system distribution is not equivalent to the average Galactic distribution, being rather the consequence of a unique injection into the protosolar nebula of matter from a massive intermediate-mass AGB star, or (3) the estimates of the temperatures in the convective shell that are given by extant models are too low by, sav, 10 or 15 percent.

The absence of carbon stars more luminous than MBOL ∼ −6 is suggested to be due primarily to the fact that ∼ 106 yr of AGB evolution is necessary to produce surface C/O > 1, rather than to be due to the burning of dredged-up carbon into nitrogen at the base of the convective envelope during the interpulse quiescent hydrogen-burning phase. Thus, the positive correlation between the nitrogen and helium abundances in planetary nebulae is perhaps primarily a consequence of the second dredge-up episode rather than a consequence of processes occurring during the thermally pulsing phase.

Among the many aspects of the evolution of low and intermediate mass stars, two representative topics are selected for this review: the question why stars become red giants, and the problem of the age determination of galactic globular clusters. Concerning the first topic, it is shown that this happens because of a thermal instability taking place in the stellar envelopes, and the physical nature of this instability is identified. Several ramifications of these findings are then briefly mentioned. Concerning the second topic, the Oosterhoff-Sandage effect is briefly described, together with its implications for the age estimates and the problems rised by its interpretation in terms of evolutionary models. In this connection, it is suggested that an enhanced overall abundance of the elements CNO and Ne may solve these problems, although further evolutionary calculations are required before reaching firm conclusions. It is also amphasized for both topics the important role played by the metal contribution to the radiative opacity at middle temperatures.

Accurate opacities for stellar composition mixtures are needed for all studies of stellar structure, evolution, stability, and pulsation. In several cases it appears that larger opacities in the range of temperature near one million kelvin would assist is resolving some current discrepancies between observations of stars and some theoretical predictions. Opacities published by Carson, Mayers, and Stibbs (1968) and more recently modified and available informally, have this larger opacity in this temperature region compared to the widely used Los Alamos opacities. See the tables of Cox and Stewart (1965, 1970ab) and Cox and Tabor (1976). It is therefore of great interest to see if the actual cause of the differences between these two sets of opacities can be found and discussed.

Accurate tests of the theory of stellar structure and evolution are available from the Sun's observations. The solar constraints are reviewed, with a special attention to the recent progress in observing global solar oscillations. Each constraint is sensitive to a given region of the Sun. The present solar models (standard, low Z, mixed) are discussed with respect to neutrino flux, low and high degree five-minute oscillations and low degree internal gravity modes. It appears that actually there do not exist solar models able to fully account for all the observed quantities.

We present here some initial results of a long-term investigation of resonant three-wave interactions in the solar interior, which indicate that these nonlinear interactions take place in the sun and are, in fact, responsible for the observed g mode spectrum. Resonant three-wave interactions, as the name implies, involve the coupled interaction of three waves which satisfy the resonant condition where ω0, and ω1 are the frequencies of the three waves. Two of the waves, mode 0 and 1 for example, couple together to produce a third beat wave which has a frequency equal to the frequency difference of the first two waves. This wave is normally very weak. If its frequency happens to equal the frequency of an oscillation mode of the sun, the wave can be pumped by resonance to very large amplitudes. In the sun, resonant interactions would take place if three natural oscillation modes of the sun satisfy the resonance condition.

Most stars contain regions which are convectively unstable and one of the more daunting tasks facing astrophysics today is to find a satisfactory theoretical formulation of turbulent energy transport in stars. Various theories have been proposed, such as the mixing-length formalism and its extensions, and it would be most useful if one could test the accuracy of such models in view of their importance in the theory of stellar structure and evolution.

We present and briefly discuss basic characteristics of a standard solar model as well as those for two series of nonstandard models computed with Paczyński's stellar evolution code.

Ages of six intermediate-age Large Magellanic Cloud star clusters have been estimated using the time dependent behavior of the luminosity of stellar interior models of red giants. All clusters studied, NGC 1783, NGC 1868, NGC 1978, NGC 2121, NGC 2209, and NGC 2231, were found to have ages < 109 yr. It is concluded that there is currently no substantial evidence for a major cluster population of large, populous clusters > 109 yr in the Large Magellanic Cloud.

Young star clusters (<3 × 108 yr) in the Maqellanic Clouds (MC) can be used to test the current status of the theory of stellar evolution as applied to intermediate and massive stars. The color-magnitude diagram of many young clusters in the MC shows, unlike the case of clusters in our Galaxy, large numbers of stars in both the main sequence and post main sequence evolutionary phases. Usina a arid of stellar evolution models, synthetic cluster H-R diagrams are constructed and compared to observed color-magnitude diagrams to determine the age, age spread, and composition for any given cluster. In addition, for those cases where the data is of high quality, detailed comparisons between theory and observation can provide a diagnostic of the accuracy of the stellar evolution models. Initial indications of these comparisons suggest that the theoretical models should be altered to include: a larger value for the mixing length parameter (α), a larger rate of mass loss during the asymptotic giant branch (AGB) phase, and possibly convective overshoot during the core burning phases.

Since some of the earliest evolutionary calculations it has been found that post main sequence stars become red giants (e.g. Sandage and Schwarzschild, 1952). However the exact physical processes that lead to and determine the rate of redward evolution are not completely understood.

In many ways, this paper can be thought of as an introduction to that of Nissen's, and others, which contain high quality, new data for open clusters, particularly for work that includes observations of stars near the turn-off from the main sequence.

Photoelectric uvby photometry has been obtained for about 30 F-type stars in each of the open clusters M67 and NGC3680. For some of the stars the H-beta index was also observed. The photometry was carried out with the Danish 1.5 m telescope at La Silla by the aid of a four-channel uvby photometer and a two channel H-beta photometer.

In order to verify the agreement with the theory of the observed HR diagram as a whole, 38 open clusters with (B-V)o, t≥0.10 at the turnoff, have been analyzed with particular regard to the RGB luminosity function.

The study of X-ray emission of stellar clusters, allows to decouple the influence of some individual stellar parameters, as initial conditions, composition and age, on the stellar X-ray luminosity function.

The best empirical evolutionary tracks are provided by open cluster HR diagrams. The scarcity of giants in young clusters implies that diagrams of clusters having similar ages and metallicities have to be summed. Using UBV data, Mermilliod (1981a) has divided the nearby open clusters into 14 age groups, and has described the properties of the composite diagrams MV/(B-V) and Mbol/log T. Several features complicate the structure of composite HRD, namely the presence of double stars which often mimic extended blue loops and the contamination by non-member stars difficult to identify as such in distant clusters. In order to refine the red giant observed evolutionary properties, cluster giants have been remeasured in the Geneva photometry and with the spectrovelocimeter CORAVEL.

Under the assumption that grain sedimentationcan lead to an enhancement of heavy elements in the central regions of proto-stars, we present the evolution of stellar models with metal-rich cores. The resulting isochrones can explain the “double-gap” clusters NGC2420 and NGC2506, without destroying the agreement for other clusters.