Red dwarf
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 turnoff the main sequence. In addition, the fact that no red dwarves off the main sequence have been observed is evidence that the universe has a finite age.
One mystery which has not be 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 dwarves, they should still be observable today, but are not. The conventional explanation is that without heavy elements, low mass stars cannot form and the first stars were extremely high mass population III stars which died quickly and produced the metals necessary 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.
This is also the title of a popular BBC science-fiction comedy series, see Red Dwarf (television).
See also