# How Wide Would the Habitable Zone Be in a Singular Red Giant System?

Astrobiologists looking for signs of life outside Earth usually take excitement over planets orbiting red giant stars because a larger, brighter star usually means a farther-away but still wider habitable zone, a slice of space where liquid water would be possible.

To put this in perspective, a single red giant can have a luminosity ranging anywhere between 1,000 and 10,000 times brighter than our sun. Would that mean that a habitable zone in a solar system orbiting only one red giant would be 1,000 to 10,000 times as wide as our own?

(The reason for the square root dependence is that a piece of surface at semimajor axis $$a$$ gets $$L/4\pi a^2$$ Watt of incoming energy, and if a blackbody with emissivity $$\epsilon$$ radiates away $$\sigma \epsilon T^4$$. Energy balance gives $$L/4\pi a^2 = \sigma \epsilon T^4$$, or rearranged, $$a = \sqrt{L/4\pi \sigma \epsilon T^4}$$, proportional to $$\sqrt{L}$$. The life zone is given by the range where $$T$$ allows liquid water. In practice this is more complex and fuzzy since it all depends on complex atmospheric properties, but as a first approximation it feels OK.)