Stars send out radiation over a wide range of frequencies, and the detection of such radiation gives information about their surface properties. For one star only, the Sun, there is additional information from the central regions, because there is the possibility of detecting certain sub-atomic particles, called neutrinos that are produced in the nuclear reactions. It is the task of stellar structure theory to explain, by means of the known laws of physics, the observed properties of a star and to fill in the gap between the inaccessible centre and the visible surface by theoretical deduction. The procedures for carrying out the necessary observations are described in chapter 2. and so we will simply draw attention to those results of particular relevance to stellar astrophysics.

The most significant observations for stellar structure theory are these:
(1) Stars radiate energy continuously.

(2) When we consider main-sequence stars, we find that the stars of a given mass have a given luminosity. This is the MASS-LUMINOSITY LAW. it implies that the energy which ultimately flows out of a star is determined by how much matter the star is made up of.

(3) In the Hertzsprung-Russell diagram stars are not scattered uniformly all over the place. Stars seem to occupy preferentially certain well-defined regions of the diagram. This teaches us that the surface temperature, or spectral type of a star is not independent of its absolute magnitude, or luminosity.

For the Sun, at least, we know from fossil remains on Earth, that it has continuously radiated energy at about the same rate as at present for about 4 X 109 years. Approximate ages can be inferred for other stars, and they run into billions of years. The most ancient stars in our Galaxy are thought to be around ten billion years old. This raises the important question of the source of stellar energy.

The mass-luminosity law. The main feature is the sharp dependence of luminosity (L) on mass (M); the rough relations are that L is proportional to M3 for high masses (over about three solar masses) and for low masses (less than half the Sun) whereas L depends on M4’5 in between. The indices 3 and 4.5 are very approximate. To illustrate the relations, consider ‘a star ten times as massive as the Sun (M = 10). This is about a thousand times as bright (i.e. L=103), which corresponds to a difference of 7.5 mag. in the absolute magnitude. The magnitudes used in figure 3.2 are, of course, absolute ones; it would not make sense to compare apparent properties which are influenced by the distance of the individual stars from Earth. were obtained from observations of binary stars, and the method of determining stellar masses is explained .

The main features of the Hertzsprung-Russell diagram are described in chapter 2. Figure 3.3 indicates schematically the features which we will need for our discussion. The figure shows the relationship of the various features to one another and where they are approximately in spectral type and absolute magnitude. In any given Hertzsprung-Russell diagram, many of the features may be absent. Of special importance to stellar evolution theory are the Hertzsprung-Russell diagrams of clusters of stars. The reason for this is as follows: the stars in a typical cluster are all at nearly the same distance from the Earth since the cluster diameter is very small compared to the cluster distance. Therefore it is not necessary to convert the measured apparent magnitudes into absolute ones because the conversion factor is the same for all the cluster members. We can therefore plot a Hertzsprung-Russell diagram for a given cluster with apparent magnitudes. Moreover it is reasonable to assume that the initial chemical compositions of all cluster members were similar, and that all the stars were born at almost the same time. Now, the observed properties of a star depend most strongly on its mass, age and chemical composition. Therefore a cluster gives an opportunity of isolating the evolutionary effects due to only one variable, the mass of a star, since the age and chemical composition are constant in a given cluster. Furthermore, different clusters at different ages, but with similar chemical compositions, enable us to investigate the effects of age. Give typical examples of the Hertzsprung-Russell diagrams of a galactic (or open) cluster and of a globular cluster. It is one of the tasks of stellar evolution theory to explain how a star changes with time and the nature of the Hertzsprung-Russell diagrams of clusters.

The observed properties of stars cover a wide range which is given in table 3.1. The Sun, which is the only star whose shape can be seen easily, is spherical and we believe most stars to be so. Rapidly rotating stars and those in close binary systems are some¬times non-spherical in their outer layers; in a detailed theory the perturbing forces which cause these odd shapes would have to be considered. We shall concentrate here on spherical stars for simplicity.

The detailed chemical composition of stars is discussed in chapters 2 and 7. For our purposes the main results are that for stars like the Sun the composition by mass is about 70 per cent hydrogen, 28 per cent helium and 2 per cent for all the other elements together, the so-called HEAVY ELEMENTS. Very old stars of Population II appear to have a much smaller amount of the heavy elements, namely about 0.1 per cent by mass. The difference in the stellar populations is not confined to chemical composition alone, but includes variations of space distribution, age, and velocity dispersion. Typically Population I-type stars have small velocity dispersion of their space motion, show a space distribution confined to the disc of the Galaxy and are relatively young. Population II objects have higher velocity dispersion, an almost spherical galactic distribution and are relatively old, The globular clusters in our Galaxy are examples of Population II objects, whereas young associations such as that in Orion are examples of Population I. The two populations are not always distinct: there is a continuum between. The origin of Population types is connected with the chemical and dynamical evolution of the galaxy

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