And the first concept to cover here is the so called HR diagram, which stands for Hertzsprung–Russell Diagram. This is why everybody calls it HR. And it is the main arena in which we study stellar evolution and the stellar models. But before we get to that, you may recall that stars have different spectral types. And they were originally classified without anybody knowing what was behind it, before atomic physics was really well developed. But they can be sorted in the order of how different spectroscopic lines appear. And now we know that those are a sequence of photospheric temperatures with so called O-stars being the hottest and M-stars being the coolest. And if you look at this, you can recognize some of the famous lines. But the cooler you go, the more lines start to show up, and that's just because those molecules are excited by those wavelengths. The hydrogen lines, which you can recognize near the top, the alpha on the right, and beta, gamma, delta, and so on, disappear by the time you get to cooler stars because there isn't enough energy to pump those energy levels of hydrogen. So now we know how to interpret this, and stellar temperature is obviously an interesting variable. So way back when, these two astronomers, Hertzsprung and Russel, after luminosities of some stars were measured by measuring their distances, discovered that if you plot a spectroscopic class, properly sorted, which really is a measure of temperature versus the luminosity or absolute magnitude, stars don't fill up that space randomly. They line up on couple different kind of quasi-linear sequences and most of them sit on circle, main sequence. Then there are giants, which are so called because they're extra bright supergiants, even more so. And there are dwarf stars or white dwarfs, which are much dimmer. So this turned out to be a really powerful tool to try to understand stellar structure in evolution. And there are different sequences here. Now we know what they are. And they are actually due to a different type of energy generation in the stellar core. The main sequence, which is where most stars spend most of their lives, has then turn-off, those are stars that they're now evolving off to become red giants, then giants can evolve off to the horizontal branch and it can come back to the asymptotic giant branch, and so on. So here is, here we have the similar plot expressed now, in a slightly different way. Now, one thing you need to keep in mind is that this correlates absolute luminosities with temperatures. Neither one of these two is directly measured. Absolute luminosity is something we have to derive after we measure flux of some magnitude and have a model of stellar atmosphere. Temperature is also something you can derive from spectroscopy or from plutometry. And, generally speaking, we don't, nowadays, we use colors as a measure of stellar temperatures. Colors are quantitatively defined as the difference of magnitudes in two different filters, because magnitudes are a logarithmic measure of flux, it actually means it's a log of the ratio of the two fluxes. And, so bluer stars will have higher blue to red ratio, and vice versa. So for example, B and V are two commonly used filters in photometry, visible light corresponding to blue, invisible light. And they can be used as an excellent proxy for stellar temperature, absolute magnitude is the most directly determined measure of luminosity if you know the distance. This particular HR diagram is for all stars, for which parallaxes were measured by the Hipparcos satellite, which pretty much is all the stars with measured parallaxes today until Gaia starts producing results. So, there is an important catch here, that if you want to compare these measured quantities with theoretical models, theoretical models give you temperature and luminosity. Those are not measured quantities, so you have to do some interpretation. And I think we know how to do this. Now, stars of different mass are in different places along main sequence, and each of them has a particular type of track, along which it moves, as it evolves. Where they end up is, form is one of these low sides, like horizontal branch or what have you.
