Barnard's star

Barnard’s star, second nearest star to the Sun (after the triple system of Proxima Centauri and Alpha Centauri’s A and B components considered together), at a distance of 5.95 light-years. It is named for Edward Emerson Barnard, the American astronomer who discovered it in 1916. Barnard’s star has the largest proper motion of any known star—10.39 seconds of arc annually. It is a red dwarf star with a visual magnitude of 9.5 and thus is too dim to be seen with the naked eye despite its close distance; its intrinsic luminosity is only 1/2,600 that of the Sun.

Super-Earth planet orbiting Barnard’s Star

Red dwarfs probably can't support plant life. The super earth planet at Barnard's star might be able to support life through geothermal heating. Because of its higher mass, the planet might be able to provide significant energy to an exosystem that doesn't need any energy from the Sun to survive.

Although likely cold (-170 degrees centigrade), it could still have the potential to harbor primitive life if it has a large, hot iron/nickel core and enhanced geothermal activity.

The planet has a mass at least 3.2 times that of Earth and orbits the star with a period of 233 days at a distance of about 60 million kilometers (37 million miles). Because of the star’s low luminosity, the planet is not in the habitable zone, and any water on its surface would likely be frozen.

An interesting bit of information is that Barnard’s star was selected by Project Daedalus as an achievable destination.