When hydrogen – burning reaction in the core are first fully supplying the radiating energy of the star it is said to be on the zero age main sequence. The star stays in the main-sequence band of the Hertzsprung-Russell diagram as long as it has hydrogen nuclear reactions in its core. In general the layers of a star do not get mixed up (helium is heavier than hydrogen). In convective zones the layers are mixed, but only in the zone itself. As evolution proceeds the hydrogen nuclear fuel in the core is being depleted and the core is becoming rich in helium. With reduced fuel, nuclear energy output is not being maintained so the core contracts, which causes a raising of the temperature and a compensating enhancement of the nuuclear reactions. For reasons not fully understood, but connected with the distribution of the total gravitational potential energy of the star, core contraction is accompanied by envelope expansion. The main-sequence phase of evolution is characterized by hydrogen depletion in the core and a slow expansion of the outer layers, that occurs on the nuclear timescale. There is a slight increase in energy output and the outer layers cool down somewhat

When all the hydrogen is exhausted in a stellar core, nuclear energy generation there stops. Without mixing, hydrogen -rich material cannot he brought down to the core. The outside of the star is still, however, radiating as before and it derives this energy from gravitational contraction of the whole star. This is the overall contraction phase of post -main -sequence stellar evolution. Half the energy from contraction goes into radiation and the other half heats up the whole star. This contraction phase continues until some part of the star becomes, hot enough for nuclear reactions to work again. There is the possibility that the very central region now made of helium will become hot enough (108K) for helium to burn to carbon. In fact what happens first is that the layers of hydrogen outside the helium core become hot enough (107K) for hydrogen to burn to helium. At this stage hydrogen burning starts to take place in a shell. The new release of energy halts the overall contraction and the energy radiated is now supplied by the nuclear energy liberated in the hydrogen burning -shell. The helium core is however, still contracting while the envelope of the star is expanding slowly.

As successive shells of hydrogen are burnt the helium produced joins the core, which grows in mass. There is a maximum pressure that the inert helium core can exert. When its mass becomes too large it collapses under its own weight and the pressure of the over¬lying layers of the star. The critical mass of the core is about one tenth the mass of the star for a star of a few solar masses. The in¬stability takes place on a thermal timescale, and core collapse is accompanied by envelope expansion. The star now increases rapidly in radius and moves to the right, lower temperature side of the Hertzsprung-Russell diagram. Stars spend only a little time in this phase of evolution, so in a cluster very few stars should be seen at this position in the Hertzsprung-Russell diagram; this region is called the Hertzsprung gap. The energy production at this phase is by hydrogen shell-burning.

The expansion and cooling of the outer layers of the star make them convective, and the star lies very near the Hayashi track in the Hertzsprung-Russell diagram. The helium core continues to contract until it becomes hot enough for the nuclear reactions of helium fusing to carbon to work. The core collapse is then stopped and there are now two energy sources: the nuclear burning of helium in the core and hydrogen in a shell further out. The star is now extremely luminous, extremely large and very cool; it is a BED GIANT.

The further evolution of a star may take it through further nuclear burnings, depending on its mass. These nuclear burnings do not produce very much energy because the changes in nuclear energy are rather small. The lifetime of a star in these phases of evolution is short. The main importance of these further reactions is the synthesis of heavy elements Much energy may be lost by neutrino emission; unfortunately no such star is close enough for these neutrinos to be detected.

Several times during its evolution after the main sequence a star may be in the instability strip which is where its temperature and luminosity are such that its outer layers are pulsationally unstable. The star then appears as a Cepheid variable star, for example (see chapter 4). The time spent in the instability strip, while the star is crossing the Hertzsprung gap, is rather small. Much more time is spent there during the core-helium-burning phase, after the star has been a red giant. Cepheids are therefore core-helium-burning stars, at a late stage of evolution, whose outer layers are pulsationally unstable. A problem of stellar evolution theory has been to reconcile the mass of a Cepheid deduced from evolution with its mass deduced from pulsation theory. There is still controversy here. The instability strip has a limited width in the Hertzsprung-Russell diagram because if the star is too cool its outer layers are convective, which destroys pulsation; on the other hand, if the star is too hot the pulsation excitation mechanism does not operate..

The details of an evolutionary track, the path taken by an evolving star in the Hertzsprung-Russell diagram. The tracks are fairly similar for different masses and the various stages of evolution are indicated in the caption. The different initial direction of evolution for the 1.0 solar mass star occurs because it has a radiative core and is converting hydrogen to helium by the p-p chain. The higher mass stars have convective cores and convert hydrogen to helium by the CN cycle.

Two important observational quantities in the Hertzsprung-Russell diagram of a cluster are the number of red giants and Cepheids compared with the number of main-sequence stars. Roughly speaking the ratio of numbers of stars should be the ratio of their lifetimes in the appropriate phases of evolution. In general the observations of clusters confirm this theoretical expectation reasonably well. The range of observed stellar masses also may be explainable. For too small a mass, the temperature does not become hot enough for nuclear reactions, and the star becomes a BLACK DWARF, producing little luminosity. For too high a mass the luminosity is so high that radiation pressure blows the star apart or prevents its formation.

The exact details of a star’s evolution depend primarily on its mass and initial chemical composition, but the general principles outlined above are broadly true. The radius of a star at the red-giant stage is roughly a hundred times its main sequence radius. This is. of special importance for the evolution of binary-star systems since, if the binary is a close binary, during certain stages of evolution mass may be exchanged between the two components.

A point that we have not yet mentioned concerns lower-mass stars. These might not ignite carbon, and when igniting helium might do so under degenerate conditions. Because of the peculiar equation of state of degenerate matter, the temperature and pres¬sure are not strongly connected. Helium ignition causes an increase in energy production which increases the local temperature, which increases the reaction rate, but without a compensatory increase in pressure. A runaway therefore develops; this is known as the HELIUM-FLASH whose consequences are uncertain. Eventually there is so much energy that degeneracy is removed; the temperature is now connected through the equation of state to the pressure and expansion relieves the situation. At the peak of the flash the nuclear reactions inside one star may be producing as much energy as a whole galaxy of stars. Almost all this energy is probably absorbed by the outer layers of the star, which expand, and very little appears at the stellar surface to increase the observed luminosity.

The shape of a Population II star evolutionary track is different from that of a Population I star. The higher heavy-element abundance in the Population I stars strongly affects their opacities and alters the evolution. In our Galaxy the shapes of globular cluster (Population II) and galactic cluster (Population I) Hertzsprung-Russell diagrams are quite different, but this is largely caused by their different ages. The globular clusters in our Galaxy were probably formed during the early stages of the collapse of our galaxy and they are about 1010yr old. Galactic or open clusters range in age from 106 to 1010 yr old. In globular clusters in our Galaxy, stars more massive than about a solar mass have already had time to evolve, whereas in an open cluster of age 107yr a star of about ten solar masses is just evolving. An important feature of the Hertzsprung-Russell diagrams of globular clusters is the HORIZONTAL BRANCH .This consists of low-mass stars that have Probably lost mass in the red-giant phase. The stars in the in¬stability strip in globular clusters are also of low mass, they are the RR Lyrae stars . In other galaxies such as the Magellanic Clouds, much younger globular clusters have been discovered which Provide important tests for the theory of stellar evolution.

Comments are closed.