Hello, I will need to talk to students about the evolution of a solar-like star. We will look at a diagram like the following: It will be a descriptive presentation, no mathematics. I know pretty well what happens until the formation of the carbon core. The linear upper line happens because the outer shells will be ejected and gradually the core will become visible so of course the temperature strongly increases (what we effectively see is the core). But why this increase in temperature is at constant luminosity, and why do we have that abrupt decrease in luminosity just before the white dwarf stage?