The distance of the habitable zone from the star will vary depending on the type of star. This criterion is not strict. A runaway greenhouse effect. So the greenhouse heats up. Greenhouse Effect on Earth Photons from the sun reach the surface of the earth.
Carbon dioxide prevents infrared photons from radiating energy to space.
The Earth can't cool. Too much CO 2 will cause the earth to get too hot. Barnard's star could not support photosynthesis. Photosynthesis not possible The Lifetime of Stars Stars must live long enough for life to evolve. O, B, and A type stars do not survive long enough for life to evolve.