The Final Stages of Evolution

The endpoints of stellar evolution can be seen from Fig. 11.8. This shows the relation between mass and central density for a body at zero temperature, i. e. the final equilibrium when a massive body has cooled. There are two maxima on the curve. The mass corresponding to the left-hand maximum is called the Chandrasekhar mass, MCh ~ 1.2-1.4 Me, and that corresponding to the right-hand one, the Oppenheimer-Volkoff mass, Mov « 1.5-2Mq.

Let us first consider a star with mass less than MCh. Suppose the mass does not change. When the nu clear fuel is exhausted, the star will become a white dwarf, which will gradually cool down and contract. In Fig. 11.8 it moves horizontally to the right. Finally it will reach zero temperature and end up on the left-hand rising part of the equilibrium curve. Its final equilibrium is a completely degenerate black dwarf.

If the mass of the star is larger than MCh but smaller than MOV, it can continue cooling until it reaches the right-hand rising section of the curve. Again there is a stable final state, this time corresponding to a completely degenerate neutron star.

An even more massive star with mass larger than MOV will go on contracting past the density correspond-

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Fig. 11.7. Evolution schemes for stars with different masses. The radius is scaled to be the same in all drawings. In reality, there are vast differences in the sizes of different stars and different phases of evolution. In the beginning (1) a gas cloud is contracting rapidly in free fall. Because the gas is quite rarefied, radiation escapes easily from the cloud. As the density increases, radiation transport becomes more difficult, and the released energy tends to warm up the gas. The contraction lasts until the gas is completely ionized, and the star, which has become a protostar, is in hydrostatic equilibrium (2). The star is convective throughout its interior.

Now evolution continues on a thermal time scale. The contraction is much slower than in the free-fall phase. The phases of further evolution are determined by the mass M of the star. For M < 0.08 M0 the temperature in the centre does not rise high enough for hydrogen burning, and these stars con

11.5 The Final Stages of Evolution tract to planetlike brown dwarfs. Stars with M > 0.08 Mq start hydrogen burning when the temperature has reached about 4 x 106 K. This is the beginning of the main sequence phase. In the main sequence, the lowest-mass stars with 0.08 Mq < M < 0.26 Mq are entirely convective, and thus they remain homogeneous (3). Their evolution is very slow, and after all the hydrogen has been burnt to helium, they contract to white dwarfs (4).

The increasing temperature makes the stars with M > 0.26 Mq radiative in the centre as the opacity decreases (J). The low-mass stars with 0.26 Mq < M < 1.5 Mq remain radiative in the centre during the main sequence phase (6) as they burn their hydrogen through the pp chain. The outer part is convective. At the end of the main sequence phase, hydrogen burning continues in a shell surrounding the helium core (7).

The outer part expands, and the giant phase begins. The contracting helium core is degenerate and warms up. At about 108 K, the triple alpha process begins and leads immediately to the helium flash (8). The explosion is damped by the outer parts, and helium burning goes on in the core (9). Hydrogen is still burning in an outer shell. As the central helium is exhausted, helium burning moves over to a shell (10). At the

same time, the outer part expands and the star loses some of its mass. The expanding envelope forms a planetary nebula (11). The star in the centre of the nebula becomes a white dwarf (12).

In the upper main sequence with M > 1.5 Mq energy is released through the CNO cycle, and the core becomes convective, while the outer part is radiative (13). The main sequence phase ends as the hydrogen in the core is exhausted, and shell burning begins (14). The helium core remains convective and nondegenerate, and helium burning begins without perturbations (1J and 19). Afterwards, helium burning moves over to a shell (16 and 20). For stars with 3 Mq < M < 15 Mq the carbon in the core is degenerate, and a carbon flash occurs (17). This leads to a supernova explosion (18) and possibly to the complete destruction of the star.

For the most massive stars with M > 15 Mq the carbon core remains convective, and carbon burns to oxygen and magnesium. Finally, the star consists of an iron core surrounded by shells with silicon, oxygen, carbon, helium and hydrogen (21). The nuclear fuel is now exhausted, and the star collapses on a dynamical time scale. The result is a supernova (22). The outer parts explode, but the remaining core continues to contract to a neutron star or a black hole

H on the surface 12

m ma

Mr m ma



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lg P

Fig. 11.8. The evolutionary end points of stars with different masses shown as a function of central density. The curve shows the behaviour of the central density of completely degenerate (T = 0 K) bodies. The Chandrasekhar mass Mch and the Oppenheimer-Volkoff mass Mov correspond to maxima on this curve

Fig. 11.8. The evolutionary end points of stars with different masses shown as a function of central density. The curve shows the behaviour of the central density of completely degenerate (T = 0 K) bodies. The Chandrasekhar mass Mch and the Oppenheimer-Volkoff mass Mov correspond to maxima on this curve ing to a neutron star. There is then no longer any known possible stable equilibrium, and the star must go on contracting to form a black hole.

The only endpoints of stellar evolution predicted by theory are the two stable states of Fig. 11.8 and the two extreme possibilities, collapse to a black hole or explosive disruption.

The preceding considerations are purely theoretical. The final evolutionary stages of real stars involve many imperfectly known factors, which may affect the final equilibrium. Perhaps most important is the question of mass loss, which is very difficult to settle either obser-vationally or theoretically. For example, in a supernova explosion the whole star may be disrupted and it is very uncertain whether what remains will be a neutron star, a black hole or nothing at all. (The structure of compact stars will be discussed in Chap. 14.)

A summary of the variuos evolutionary paths is given in Fig. 11.7.

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