lec-17 - Lecture 17: Stellar Evolution (I) The life cycle...

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Lecture 17: Stellar Evolution (I) The life cycle of low-mass ( M . 8 M ± I. Stellar Models: Beyond the Sun In Lecture 15 I wrote down the stellar structure equations. They can be applied not only to the Sun, but also to other kinds of stars. According to the Vogt-Russell theorem, once you specify the mass and composition, everything else follows. Mass is most important; composition is secondary, because stars have compositions that are relatively similar. For hydrogen burning stars, you can use the model to compute the luminosity and effective temperature as a function of mass, and you find the diagram on the left: ! 0.4 0.0 0.4 0.8 1.2 1.6 2.0 16 12 8 4 0 ! 4 ! 8 B ! V M V B0 A0 F0 G0 K0 M0 O5 M8 Giants Supergiants White dwarfs Main sequence Figure 1: Theoretical (left) and observed (right) HR diagrams. (From Figs. 10.13 and 8.13 This matches up well with the main sequence in the observed HR diagram. In other words, main sequence stars are burning hydrogen, and the sequence goes from massive, hot, luminous stars in the upper left to low-mass, cool, faint stars in the lower right. Physically, the key concept is that as the mass increases, the gravity increases, so the tem- perature must increase to balance gravity. As the temperature goes up, so too does the fusion rate, and hence the energy output or luminosity. To the extent that main sequence stars have similar compositions, mass controls pretty much everything. What sets the endpoints of the main sequence? As the mass decreases the temperature also decreases. At some point the central temperature is too low to support fusion. This is the bottom end of the main sequence — the lowest mass object we call a star. The models indicate that the fusion limit occurs around 0 . 08 M ± . I will make an estimate of this number 1
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below. At the upper end, above about 90 M ± the fusion is so intense that the radiation pressure makes the core unstable. In between these extremes, I already mentioned (Lecture 14) that around 1 . 2 M ± there is the transition from PP-driven fusion to CNO-driven fusion. To summarize, we can make a table like this: Mass ( M ± ) Fusion Convection . 0.08 no fusion 0.08–0.3 PP fully convective 0.3–1.2 PP surface convection 1.2–90 CNO core convection 90 unstable Note that low-mass stars are common and high-mass stars are rare, so what happens at the low-mass end is quite important. What about convection? For massive stars, the CNO fusion rate depends so strongly on temperature that the energy production rate changes very rapidly with radius. Radiation is unable to move the energy fast enough, so convection kicks in to get the energy out of the core. For stars like the Sun, the PP fusion rate is less dependent on temperature, so the energy
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lec-17 - Lecture 17: Stellar Evolution (I) The life cycle...

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