The progress in the investigation of the spectrum-luminosity diagram. The spectrum-luminosity diagram, or the Hertzsprung-Russell diagram, is of extreme importance in stellar astronomy, astrophysics and stellar cosmogony. A number of stellar characteristics can be read from the diagram, as well as the theoretical paths of stellar evolution. A very significant problem is the improvement of the diagram, i.e. the accumulation of more precise data concerning the subdivision into sequences, the contours of the latter (mean lines, dispersions, gaps) and other characteristics (masses, axial rotations, chemical composition, space-kinematical properties).

The most important relationship between physical characteristics of stars is the spectrum-luminosity correlation. Investigating the character of this correlation for stars of open clusters, Trumpler has worked out a classification of clusters according to their spectral composition.

The color-magnitude diagrams of globular star clusters are described and attention is called to some evolutionary implications. The predominant stellar population of large elliptical galaxies is shown to be unlike that of globular star clusters but probably similar to that of the older stars in the disk of our Galaxy. The same is true of the population in the nuclei of spiral galaxies. Dwarf ellipticals, on the other hand, are found to have a globular-cluster-type population. The kind of stellar population predominant in a galaxy seems to depend upon the magnitude and the rotational flattening of the galaxy. A unified evolutionary hypothesis is proposed to account for the existence of galaxies of different types.

Sub-luminous stars of high temperature show a wide variety of spectra and physical properties. Vorontsov-Velyaminov has called this region of the HR diagram the “blue-white sequence”. I wish to discuss the fainter members of this class. The growth of knowledge of colors and spectra has been rapid compared to that of the luminosities, and unfortunately only rough location in the HR diagram is yet possible. Figure 1 shows the general location and subdivision of sub-luminous stars. I shall discuss:

1. (1) Old novae.

2. (2) Horizontal-branch stars.

3. (3) Hot subdwarfs.

4. (4) White dwarfs.

Modern photoelectric techniques yield magnitudes and colors of stars with accuracies of the order of a few thousandths and a few hundredths of a magnitude respectively. Hence for star clusters it is possible to derive highly accurate color-magnitude arrays since all of the members of a cluster may be considered to be at the same distance from the observer. It is much more difficult to do this for the nearby stars where all of the objects concerned are at different, and often poorly determined, distances. If one depends upon trigonometric parallaxes, the bulk of the reliable individual values will refer to main sequence stars, and while the mean luminosities of brighter stars are given reasonably well by this method, the scatter introduced into a color-magnitude array by using individual trigonometrically determined luminosities could obscure important features. Somewhat similar objections could be raised against the use of the usual spectroscopic parallaxes which also should be quite good for the main sequence but undoubtedly exhibit appreciable scatter for some, at least, of the brighter stars.

One of the most important points in the study of the problem of the origin and evolution of stars is a detailed analysis of the structure of the HR diagram as a whole, and the structure of its separate sequences.

Combined spectroscopic and photo-electric observations of bright stars in the two Magellanic Clouds show that:

1. 1) There is no marked difference between the stars observed in the two Clouds when compared with each other or with normal galactic supergiants, as judged by:

   1. (a) direct spectroscopic comparison,

   2. (b) Hertzsprung-Russell diagram,

   3. (c) U, B, V plot.

2. 2) Stars observed in both Clouds suffer a small amount of absorption, the precise amount depending on the intrinsic colours adopted. How much of the absorption takes place within the Clouds remains to be determined.

3. 3) A reddening path has been determined by comparison of Cloud stars (little reddened) and galactic supergiants (heavily reddened). The observations are consistent with a single reddening path and have not yet suggested any difference in the absorbing properties of dust in the Clouds and in the Galaxy. A conclusion on this latter point must await observations of heavily reddened stars in the Clouds.

In 1957 a two-year photometric study of the Small Magellanic Cloud, sponsored by Indiana University and supported by the National Science Foundation was completed. Six region swere investigated. They are three on the edge of the SMC centered on conspicuous star clusters and three nearer the center.

The principal basic parameters of early-type stars being mass and age, two-dimensional classification according to the MK system corresponds to a mass-age classification.

The theory of the stellar interior indicates that for a star of given mass, given initial composition, and given age, all physical characteristics (including the luminosity and the effective temperature) are uniquely determined. Accordingly it should be possible to derive theoretically for a particular star of definite mass and initial composition a relation between luminosity and effective temperature, i.e., a curve in the Hertzsprung-Russell diagram along which the star must move during its evolution. With the help of such evolution curves it must then be possible to identify any observed star as to its mass, composition and age. This identification is possible at present only for certain stellar types, for two reasons. First, the theoreticians have not yet succeeded in deriving all the necessary evolution curves. Second, the evolution curves cross over each other in a complicated pattern in the Hertzsprung-Russell diagram so that observations in the two dimensional Hertzsprung-Russell diagram will not always suffice to identify uniquely the state of an individual star although it appears to suffice for the identification of a whole sequence of stars, like those which are observed in stellar clusters.

This communication is concerned with recent computations made with the aid of the IBM 704. The problem was set up in collaboration with C. B. Haselgrove, using a method already described in detail. Facilities for making the computations were generously provided by the IBM Corporation.

By a “steady” evolution of a star is understood such a change of its main parameters in the flow of time, which occurs in the range of an assumed equilibrium model and is caused by regular interior processes. So, for instance, the gradual conversion of hydrogen into helium in the convective core of a star, whose substance is not mixed fully, leads to a continuous change of its luminosity, radius, Tc and ρc, convective core dimensions. However, all these changes occur all the time in the limits of the model's state of equilibrium, and the structure of the star (radiative envelope and convective core) remains unchanged until a certain limit is reached in the ratio.

The initial luminosity function ψ(Mv) was introduced by Salpeter. He assumed uniform formation of stars and derived the initial luminosity function from the observed main-sequence luminosity function and the life time of a star of magnitude Mv on the main sequence. Recently van den Bergh considered the depletion of the interstellar gas by star formation. He found that at a constant rate of star formation the gas in the solar vicinity will be exhausted about 7 × 108 years from now.

For satisfactory tests of the theory of the evolution of the massive stars, accurate data are required on their positions in the HR diagram together with the corresponding ages. The following remarks deal with two pieces of information relevant to this problem.

On high-dispersion spectrograms of some luminous M giants, the zero-volt lines of all abundant atoms and ions are double. (Fig. 1 (a), Pl. I, p. 112). This spectroscopic peculiarity was discovered by W. S. Adams and Miss MacCormack (1935), who wrote that “a possible explanation of the origin of the abnormal lines…… may be an envelope of gas surrounding the stars and expanding with a moderate velocity”. Recently it was found that some of the abnormal lines which occur in the M 5 II star α Herculis can also be seen in the spectrum of its visual companion, a giant G-type star. In this system, it is clear that the Adams-MacCormack model is correct: both stars are enveloped in gas that has been ejected from the M star (Fig. 2). Moreover, the circumstellar envelope of α Herculis must measure at least 2000 astronomical units in diameter, and in it the gas velocity exceeds the velocity of escape. The M star is clearly losing mass to the interstellar medium at a rate that has been estimated to be a about 10−7 solar masses per year.

Considerations regarding the evolutionary path of the main sequence stars depend essentially on the theorem of Vogt-Russell. According to this theorem the structure of stars with thermonuclear sources of energy is determined uniquely by their masses and chemical composition, as characterised by the mean molecular weight X, Y, Z being the relative amounts of hydrogen, helium and of the mixture of the heavy elements.