Brown dwarfs are usually not considered stars, so they are not on the main sequence.[/QOUTE]
That is not a very good reason. In principle we can put any object in the Universe we like on the HR diagram, even though they have nothing to do with stellar evolution. Besides: brown dwarfs get their energy from gravitational contraction, just as some stars do in some parts of their life, so I would think they fit perfectly well on there in the same context.
Vanadium 50 said:
There is no observational evidence as to what red dwarfs do when they leave the main sequence, since the universe is not old enough to have any examples. For the same reason, it's not been of intense theoretical interest.
There is _plenty_ of theoretical interest in low mass stellar evolution. The Universe is not old enough, so indeed we cannot find these objects, but that does not mean that we cannot calculate these objects. And we do. If stars leave the main sequence (i.e. did _did_ burn hydrogen in their core), they would indeed move upwards, along the Hayashi line: their core contracts, their envelope grows, so it cools down. They will become small variations of red giants. If they do not have enough mass to fuse helium, I guess they would just fade from there (and do some deuterium burning first).
Brown dwarfs will never move upwards, as they won't run out of the hydrigen they cannot even start burning. They will just cool down and fade.
