Abstract
I would like to start with a short historical introduction. In 1938 thermonuclear reaction rates for hydrogen burning became available. This made it possible to fit a convective core into the point source model of stellar structure integrated by Cowling three years earlier. The free parameter in the fitting process could be fixed with the thermonuclear reaction rates, the first realistic stellar model for a massive main sequence star was constructed! After the war electronic computers became available, and one was able to do more complicated models like those on the lower main sequence, like realistic models for the sun with its helium enriched interior, and one tried already to follow in time the exhaustion of hydrogen in the central regions of stars numerically. There was not too much progress for stars at the upper end of the main sequence. As soon as the stellar model tried to leave the main sequence and to march towards the region of the red supergiants the methods known at that time failed to produce models. For less massive stars the exhaustion of hydrogen could be followed up more easily and, in 1955, the great paper by Hoyle and Schwarzschild came out, which showed how these stars from the main sequence move into the red giant branch and move up parallel to what we now call the Hayashi line (which was not yet known at that time). But when helium started to burn the methods also failed.
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Kippenhahn, R. (1982). Evolution of Stars in the Post-Main Sequence Stage. In: Kopal, Z., Rahe, J. (eds) Binary and Multiple Stars as Tracers of Stellar Evolution. Astrophysics and Space Science Library, vol 98. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7861-4_1
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