An Upper Limit on the Ratio Between the Extreme Ultraviolet and the Bolometric Luminosities of Stars Hosting Habitable Planets

A large number of terrestrial planets in the classical habitable zone of stars of different spectral types have already been discovered and many are expected to be discovered in the near future. However, owing to the lack of knowledge on the atmospheric properties, the ambient environment of such planets are unknown. It is known that sufficient amount of Extreme Ultraviolet (EUV) radiation from the star can drive hydrodynamic outflow of hydrogen that may drag heavier species from the atmosphere of the planet. If the rate of mass loss is sufficiently high, then substantial amount of volatiles would escape causing the planet to become uninhabitable. Considering energy-limited hydrodynamical mass loss with an escape rate that causes oxygen to escape alongwith hydrogen, an upper limit for the ratio between the EUV and the bolometric luminosities of stars which constrains the habitability of planets around them is presented here. Application of the limit to planet-hosting stars with known EUV luminosities implies that many M-type of stars should not have habitable planets around them.