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# 12.24 Stellar Structure

There is an enormous difference between a puny red dwarf on the main sequence, barely hot enough to sustain fusion reactions, and a massive blue main sequence star, pumping out energy at a billions of times faster rate. In this spectrum, the Sun occupies the middle ground. Can we understand these differences in terms of simple physics? Yes. The structure of a main sequence star of any mass is governed by four considerations: conservation of mass, conservation of energy, hydrostatic equilibrium or the balance between pressure and gravity, and the way energy is transported or the relation between energy flow and the temperature gradient. Notice that rate of energy generation by fusion is not a primary consideration! That’s what let theorists like Eddington and Russell work out the structure of stars in the 1930s, before the fusion process was fully understood.

We’ve seen that main sequence stars have a luminosity that increases strongly with increasing mass, leading to that huge difference between high and low mass stars on the main sequence. For high mass stars, the primary way energy travels out through the star is as radiation. For low mass stars, it travels outwards by convection, or wholesale motions of the plasma.The interiors of stars are extremely hot, millions of degrees. The fall-off to surface temperatures thousands or tens of thousands of degrees takes place in a thin outer shell. Energy generation by fusion takes place in a small central region, involving a small fraction of the total mass of the star. The rapid fall-off of nuclear energy generation reflects the fact that it is very sensitive to temperature. Stars less massive than the Sun generate most of the energy by the proton-proton chain. Stars most massive than the Sun generate most of their energy by the CNO Cycle. When the details of energy transport are calculated, it turns out that massive stars are hotter in cores but actually less dense than low mass stars.

Stars are in equilibrium while they are on the main sequence. Suppose the fusion rate increases slightly. The temperature and pressure would increase, the core would expand slightly, which would lower the density and temperature, decreasing the fusion rate. so a feedback mechanism stops the fusion rate from skyrocketing. The reverse argument works as well. Stars are steady sources of radiation and light. But suppose there was no energy generation in the core. In this case, the pressure would be high and the core would be hotter than the outer envelope. Energy would escape by radiation or convection and so the core would shrink a bit by gravity. That would make it hotter, so even more energy would escape. Now it's a positive feedback loop so the effect is amplified not suppressed. The core collapses! That’s why dramatic changes occur when a main sequence star exhausts its hyrogen, and any time a star reaches the end of its nuclear fuel.