Search

In this paper the final stage of stellar evolution is studied from a theoretical point of view. Two types of stellar instabilities (hydrostatic instability and dynamical instability) are studied. It is concluded that at a temperature of T ∼ 6 × 109 °K, both hydrostatic instability, which is induced by the photodisintegration of iron into helium (phase change), and dynamical instability, which is induced by the annihilation process of neutrino production, can cause a star to collapse to beyond recovery. Moreover, neutrino processes involving electron-neutrinos and μ-neutrinos prohibit any temperature rise in the star during the collapse phase. Hence the collapse will take place under zero temperature conditions (kT ⪡ Fermi energy of electrons). The structure of static, zero temperature stars is reviewed. When the density is less than 108 gm/cm3 the star is composed of ordinary ionized nuclei. When the mass approaches 1.4 M⊗ (M⊗ = solar mass = 2 × 1033 gm) the density reaches a value that the electron zero point energy (Fermi energy) exceeds the energy difference between isobars. Inverse beta reactions then take place, decreasing the number of electrons, causing instability (hydrostatic instability). Because of this instability, no star exists whose density ranges from 109 to 1013 gm/cm3. After a density of 1013 gm/cm3 is reached, inverse beta reactions have eliminated all but a very small number of electrons. No nuclei can exist and the star is predominantly made of neutrons (neutron stars). Such a high concentration of mass produces a large curvature of space-time near the star. General relativity theory is used to describe the structure of such stars. General relativity theory predicts the existence of singularities. Two kinds of gravitational singularities may exist, according to a static, general relativistic description of cold stars. One kind of singularity corresponds to a classical situation that, at the center of such a star the gravitational potential of a test body is equal to its rest energy. Hence matter “disappears” through this kind of singularity. The other singularity corresponds to the same situation except the whole star “cuts itself off” from the rest of the universe by producing a large curvature near the star such that not even photons may leave it. However, it is indicated by work done in the past that a static description is probably unrealistic. Even in a gedanken sense, slowly adding material to a star will inevitably cause it to collapse dynamically. No completely satisfactory solution for a dynamically collapsing star has been found. The fate of collapsing massive stars (which are believed to be related to supernovae which occur at a rate of around one per hundred years per galaxy) is hence unknown, even in a theoretical sense. The surface of the remains of such stars, if visible at all, will have a temperature of around 106 °K–107 °K. Most of the radiation from such stars will be in the x-ray band and will not penetrate through our atmosphere. Hence, for the detection of such stars an orbiting telescope working in the near x-ray band will be most useful.

The paper deals with the processes of star formation under existing conditions in the galaxy. The raw material is that of interstellar clouds and attention is called to the inference that this material is probably mainly in the form of molecular hydrogen throughout most of the processes considered. It is found that a cloud having a mass of about 1000 solar masses may well be brought to the point of gravitational collapse by the pressure exerted by ‘hot’ interstellar material, but there is no known agency that is capable of causing a much smaller mass of the raw material to collapse. It is inferred that the material destined to form an entire galactic stellar cluster undergoes gravitational contraction as a whole. This leads to particular instances of the well-known problems in cosmogony of fragmentation and of the disposal of angular momentum . It is suggested that these problems, and others, find a natural solution if the raw material at a suitable stage may be regarded as broken up into ‘floccules’ in a state of chaotic supersonic motion. Then a condensation is formed simply from floccules that happen to be moving towards it. Thus conditions suitable for the production of any star exist only as conditions for the production of a number of stars, this being probably the fundamental reason for the cluster-origin of stars. These ideas have been found to offer what appears to be a promising theory of the origin of the solar system. Finally, reasons are briefly stated for the possible validity of the adopted representation of the state of motion of the medium by the concept of floccules.

The two oldest known open clusters, NGC 188 and M67, are observed to have a higher heavy-element abundance than the sun and the stars in the Hyades. This observation might be explained by assuming that these clusters were formed from unusually dusty and hence metal-rich interstellar clouds. Alternatively it may be supposed that the radiation pressure produced by stars in the spiral arms of the Galaxy ejected dust from high-latitude clouds. The calculations presented in this paper show that the loss of dust from such clouds might just be sufficient to produce a significant decrease in the mean heavy-element abundance of the interstellar gas. According to this picture, the first burst of star formation in the Galaxy led to a rapid increase in the interstellar heavy-element abundance. Subsequently, the metal abundance of the interstellar gas decreased due to the radiation pressure by young stars. The present rate of change of the heavy-element abundance in the Galaxy depends on the ratio of heavy-element production by stars to ejection of these elements by radiation pressure on dust grains. Since noble gases do not condense on grains, the neon abundance in the interstellar gas should be a monotonously increasing function of time. The observation that the neon abundance in the sun is much lower than that in young stars and nebulae lends some support to the suggestion that ejection of grains from the Galaxy effects the heavy-element abundance in the interstellar gas.

The current views of stellar evolution allow us to date galactic clusters on the basis of their color-magnitude diagrams. The youngest known clusters, those containing O-type stars, are at most a few million years old. Obviously such clusters must be continually forming unless we are at the unlikely epoch when star formation has ceased. It would be important to know if these clusters and associations represent the only regions of star formation or whether individual stars may form in the general field. The data are not available to answer this question for all stars. It is the purpose of this paper to> consider a simpler case ; do the Oand B-type stars form only in clusters and associations ? A direct approach to this question is the comparison of the expected total numbers of B and O stars computed on the assumption that they are formed only in clusters and associations with their observed total numbers.