The Giant Phase

The main-sequence phase of stellar evolution ends when hydrogen is exhausted at the centre. The star then settles in a state in which hydrogen is burning in a shell surrounding a helium core. As we have seen, the transition takes place gradually in lower main-sequence stars, giving rise to the Subgiant Branch in the HR diagram, while the upper main-sequence stars make a rapid jump at this point.

The mass of the helium core is increased by the hydrogen burning in the shell. This leads to the expansion of the envelope of the star, which moves almost horizontally to the right in the HR diagram. As the convective envelope becomes more extensive, the star approaches the Hayashi track. Since it cannot pass further to the right, and since its radius continues to grow, the star has to move upwards along the Hayashi track towards larger luminosities (Fig. 11.3). The star has become a red giant.

In low-mass stars (M < 2.3 Mq), as the mass of the core grows, its density will eventually become so high that it becomes degenerate. The central temperature will continue to rise. The whole helium core will have a uniform temperature because of the high conductivity of the degenerate gas. If the mass of the star is larger than 0.26 Mq the central temperature will eventually reach

about 100 million degrees, which is enough for helium to burn to carbon in the triple alpha process.

Helium burning will set in simultaneously in the whole central region and will suddenly raise its temperature. Unlike a normal gas, the degenerate core cannot expand, although the temperature increases (c.f. (10.16)), and therefore the increase in temperature will only lead to a further acceleration of the rate of the nuclear reactions. When the temperature increases further, the degeneracy of the gas is removed and the core will begin to expand violently. Only a few seconds after the ignition of helium, there is an explosion, the helium flash.

The energy from the helium flash is absorbed by the outer layers, and thus it does not lead to the complete disruption of the star. In fact the luminosity of the star drops in the flash, because when the centre expands, the outer layers contract. The energy released in the flash is turned into potential energy of the expanded core. Thus after the helium flash, the star settles into a new state, where helium is steadily burning to carbon in a nondegenerate core.

After the helium flash the star finds itself on the horizontal giant branch in the HR diagram. The exact position of a star on the horizontal branch after the helium flash is a sensitive function of its envelope mass. This in turn depends on the amount of mass lost by the star in the helium flash, which can vary randomly from star to star. While the luminosity does not vary much along the horizontal branch, the effective temperatures are higher for stars with less mass in the envelope. The horizontal branch is divided into a blue and a red part by a gap corresponding to the pulsational instability leading to RR Lyrae variables (see Section 13.2). The form of the horizontal branch for a collection of stars depends on their metal-abundance, in the sense that a lower metal abundance is related to a more prominent blue horizontal branch. Thus the blue horizontal branch in globular clusters with low metal-abundances is strong and prominent (Section 16.3). For stars with solar element abundances the horizontal branch is reduced to a short stump, the red clump, where it joins the red giant branch.

In intermediate-mass stars (2.3 Mq < M < 8 Mq), the central temperature is higher and the central density lower, and the core will therefore not be degenerate. Thus helium burning can set in non-catastrophically as

the central regions contract. As the importance of the helium burning core increases, the star first moves away from the red giant branch towards bluer colours, but then loops back towards the Hayashi track again. An important consequence of these blue loops is that they bring the star into the strip in the HR diagram corresponding to the cepheid instability (Section 13.2). This gives rise to the classical cepheid variables, which are of central importance for determining distances in the Milky Way and to the nearest galaxies.

In the most massive stars helium burning starts before the star has had time to reach the red giant branch. Some stars will continue moving to the right in the HR diagram. For others this will produce a massive stellar wind and a large mass loss. Stars in this evolutionary phase, such as P Cygni and n Carinae, are known as luminous blue variables, LBV, and are among the brightest in the Milky Way. If the star can retain its envelope it will become a red supergiant. Otherwise it will turn back towards the blue side of the HR diagram, ending up as a Wolf-Rayet star.

The asymptotic giant branch. The evolution that follows core helium burning depends strongly on the stellar mass. The mass determines how high the central temperature can become and the degree of degeneracy when heavier nuclear fuels are ignited.

When the central helium supply is exhausted, helium will continue to burn in a shell, while the hydrogen burning shell is extinguished. In the HR diagram the star will move towards lower effective temperature and higher luminosity. This phase is quite similar to the previous red giant phase of low-mass stars, although the temperatures are slightly hotter. For this reason it is known as the asymptotic giant branch, AGB.

After the early phase, when the helium shell catches up with the extinguished hydrogen shell, the AGB star enters what is known as the thermally pulsing phase, where hydrogen and helium shell burning alternate. A configuration with two burning shells is unstable, and in this phase the stellar material may become mixed or matter may be ejected into space in a shell, like that of a planetary nebula.

The thermally pulsing AGB coninues until radiation pressure has led to the complete expulsion of the outer layers into a planetary nebula. Low- and intermediate-mass giants (M < 8 Me) never become hot enough to ignite carbon burning in the core, which remains as a carbon-oxygen white dwarf.

The End of the Giant Phase. After the end of helium burning the evolution of a star changes character. This is because the nuclear time scale at the centre becomes short compared to the thermal time scale of the outer layers. Secondly, the energy released in nuclear reactions will be carried away by neutrinos, instead of being deposited at the centre. In consequence, while the thermonuclear burning follows the same pattern as hydrogen and helium burning, the star as a whole does not have time to react immediately.

In stars with masses around 10 Me either carbon or oxygen may be ignited explosively just like helium in low-mass stars: there is a carbon or oxygen flash. This is much more powerful than the helium flash, and may make the star explode as a supernova (Sects. 11.5 and 13.3).

For even larger masses the core remains non-degenerate and burning will start non-catastrophically as the core goes on contracting and becoming hotter. First carbon burning and subsequently oxygen and silicon burning (see Sect. 10.3) will be ignited. As each nuclear fuel is exhausted in the centre, the burning will continue in a shell. The star will thus contain several nuclear burning shells. At the end the star will consist of a sequence of layers differing in composition, in massive stars (more massive than 15 Me) all the way up to iron.

The central parts of the most massive stars with masses larger than 15 Me burn all the way to iron 56Fe. All nuclear sources of energy will then be completely exhausted. The structure of a 30 solar mass star at this stage is schematically shown in Fig. 11.5. The star is made up of a nested sequence of zones bounded by shells burning silicon 28Si, oxygen 16O and carbon 12C, helium 4He and hydrogen *H. However, this is not a stable state, since the end of nuclear reactions in the core means that the central pressure will fall, and the core will collapse. Some of the energy released in the collapse goes into dissociating the iron nuclei first to helium and then to protons and neutrons. This will further speed up the collapse, just like the dissociation of molecules speeds up the collapse of a protostar. The collapse takes place on a dynamical time scale, which, in the dense stellar core, is only

Fig. 11.5. The structure of a massive star (30 Mq) at a late evolutionary stage. The star consists of layers with different composition separated by nuclear burning shells

a fraction of a second. The outer parts will also collapse, but more slowly. In consequence, the temperature

Fig. 11.6. The usual endpoint for the development of a star with a mass of less than three solar masses, is a white dwarf, with an expanding planetary nebula around it. On the left, the planetary nebula NGC 6369, photographed with the 8-meter Gemini South telescope. For a massive star, the life ends with

Fig. 11.6. The usual endpoint for the development of a star with a mass of less than three solar masses, is a white dwarf, with an expanding planetary nebula around it. On the left, the planetary nebula NGC 6369, photographed with the 8-meter Gemini South telescope. For a massive star, the life ends with

will increase in layers containing unburnt nuclear fuel. This will burn explosively, releasing immense amounts of energy in a few seconds, principally in the form of neutrinos.

The final stages of stellar evolution may be described as an implosion of the core, which is briefly halted every time a new source of nuclear fuel becomes available for burning It is still an open problem how exactly the energy released in this collapse is transformed into the disrupton of the entire star and the ejection of its outer layers. It is also still unclear whether in a given case the remnant will be a neutron star or a black hole.

Although the exact mechanism is not yet understood, the end-point of the evolution of stars more massive the about 8 Mq is that the outer layers explode as a supernova. In the dense central core, the protons and electrons combine to form neutrons. The core will finally consist almost entirely of neutrons, which become degenerate because of the high density. The degeneracy pressure of the neutrons will stop the collapse of a small mass core. However, if the mass of the core is large enough, a black hole will probably be formed.

a supernova explosion. On the right, the supernova remnant Cassiopeia A on radio wavelengths. The image was created by the VLA telescope. (Images Gemini Observatory/Abu Team/NOAO/AURA/NSF and NRAO/AUI)
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