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Contrary to Earth, which has a small orbital eccentricity, some exoplanetsdiscovered in the insolation habitable zone (HZ) have high orbitaleccentricities (e.g., up to an eccentricity of $\sim0.97$ for HD~20782~b). Thisraises the question of the capacity of these planets to host surface liquidwater. In order to assess the habitability of an eccentric planet, the meanflux approximation is often used. It states that a planet on an eccentric orbitis called habitable if it receives on average a flux compatible with thepresence of surface liquid water. However, as the planets do experienceimportant insolation variations over one orbit and even spend some time outsidethe HZ for high eccentricities, the question of their habitability might not beas straightforward. We performed a set of simulations using the Global ClimateModel LMDz, exploring the limits of the mean flux approximation when varyingthe luminosity of the host star and the eccentricity of the planet. We computedthe climate of tidally locked ocean covered planets with orbital eccentricityfrom 0 to 0.9 receiving a mean flux equal to Earth's, around stars ofluminosity ranging from $L_\odot$ to $10^{-4}~L_\odot$. Using here a definitionof habitability based on the presence of surface liquid water, we find thatmost of the planets considered can sustain surface liquid water on the daysidewith an ice cap on the nightside. However, for high eccentricity and highluminosity, planets cannot sustain surface liquid water during the wholeorbital period. They completely freeze at apoastron and when approachingperiastron an ocean appears around the substellar point. We conclude that thehigher the eccentricity and the higher the luminosity of the star, the lessreliable the mean flux approximation.

Habitability of planets on eccentric orbits: the limits of the mean flux approximation