Stars can be divided up and classified in a number of different ways. The three main ways are by color (more specifically by the color in which the star appears brightest), by overall brightness, and by evolutionary state. Usually we have to use at least two of these classifications to uniquely describe a star - saying a star is red is fine, but unless we know whether the star is red and bright or red and faint, we won’t know what type of star exactly we’re dealing with.
Astronomers have found that we can plot all three of these things on what’s called a Hertzsprung-Russell (or H-R) diagram, named after the two people who developed it. This diagram plots brightness against colour, and stars fall on these axes in a unique way. As stars age, they will also move around on this diagram in a unique way (which can now be predicted by theoretical models). This means that the location of a star on the H-R diagram can give us all three pieces of information - colour and brightness (somewhat obviously, since we need those to plot on the diagram), but also the evolutionary state.
Colour is often broken up into a series of spectral types, labeled with the obtuse OBAFGKM scheme - you may have heard the mnemonic “Oh Be A Fine Girl/Guy Kiss Me” to help remember the order. (I prefer the alternate “Only Bored Astronomers Find Gratification Knowing Mnemonics”, but that’s just me.) Fundamentally, this breaks the blue stars (classified with O & B) from the redder ones, which tend to hang out in K & M classifications. Our sun, for reference, is a G type star. A and F stars fill in the gaps between blue and yellow - technically this is “green” but those stars would appear white to us, so they’re often color coded white instead.
Brightness at fixed color basically tells us about the size of the star. If you have two objects that are the same colour, and one is brighter, then there must be more surface area putting out that light, and therefore the star must be larger.
Within this diagram we can draw little ovals and give names to certain classes of stars. Anything along the main diagonal line going from bright blue to dim red is a “main sequence star”. These are basically normal stars - the higher up you get, the shorter a life you get. Bright blue stars (blue supergiants and blue giants) burn through their fuel very quickly, and tend to explode into a supernova in relatively short order. Red dwarfs, on the other end of the main sequence, will burn their hydrogen much more slowly, and live for billions of years. Even further off in the bottom right corner, we’d find the brown dwarfs, which are even fainter and redder than the red dwarfs. (If you’re curious about the dwarf stars in particular, there was a post all about dwarf stars recently!)
Then we have red giants and red supergiants, which live in the top right corner of this diagram. These are stars which used to be on the main sequence, but burnt through all the hydrogen available to them in their cores. Since the balance between energy creation and gravity is changing, these stars can expand quite rapidly, eventually reaching pressures in their cores which allow them to burn helium. They will continue expanding & burning until they run out of fuel and do not have the pressure required to burn the next set of elements. They appear near the top of the diagram because they’re huge - a lot of surface area puts out a lot of light.
Down in the bottom left we find the white dwarfs - these are the remains of red giant stars that have moved on to their final state. These fall in the bottom corner because they’re incredibly small, so they don’t produce a lot of light. They are, however, incredibly hot, and glow white, which pushes them to the left.
In principle, you could split this diagram up into a grid, and find something interesting and unique about the stars that fall in each grid, but as a starting point, this kind of coarse division works pretty well.
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