What is a red dwarf?

Simple answer:

It is a star that is not massive enough to initiate helium fusion, instead it just burns hydrogen at a very slow rate. Red dwarf's are the most common and longest lived stars known. [See related link for more information]

More complex answer:

According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type. They constitute the vast majority of stars and have a diameter and mass of less than one third that of the Sun (down to 0.08 solar masses, which are brown dwarfs) and a surface temperature of less than 3,500 K. They emit little light, sometimes as little as 1/10,000th that of the sun. Due to the slow rate at which they burn hydrogen, red dwarfs have an enormous estimated lifespan; estimates range from tens of billions up to trillions of years. Red dwarfs never initiate helium fusion and so cannot become red giants; the stars slowly contract and heat up until all the hydrogen is consumed. In any event, there has not been sufficient time since the Big Bang for red dwarfs to evolve off the main sequence.

The fact that red dwarfs remain on the main sequence while older stars have moved off the main sequence allows one to date star clusters by finding the mass at which the stars turn off the main sequence. In addition, the fact that no red dwarfs have evolved off the main sequence has been observed as evidence that the universe has a finite age.

One mystery which has not been solved as of 2004 is the lack of red dwarf stars with no metals (in astronomy a metal is any element other than hydrogen and helium). The Big Bang model predicts the first generation of stars should have only hydrogen, helium, and lithium. If such stars included red dwarfs, they should still be observable today, but are not. The conventional explanation is that without heavy elements, low mass stars cannot form. Since a low mass star fuses hydrogen in the presence of metals, then an early protostar of such a low mass devoid of metals would not 'go nuclear', it would simply sit around as a clump of gas until more material came along. This supports the theory that the first stars were extremely high mass population III stars which died quickly and produced the metals necessary for low mass stars to form later.

Red dwarf stars are believed to be the most common star type in the universe. Proxima Centauri, the nearest star to the Sun, is a red dwarf (Type M5, magnitude 11.0), as are twenty of the next thirty nearest. However, due to their low luminosity, few are known.

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Red dwarf is also a British sci fi TV series.