Inner Habitable Zone Boundary for Eccentric Exoplanets

The climate of a planet can be strongly a ected by its eccentricity due to variations in the stellar ux. There are two limits for the dependence of the inner habitable zone boundary (IHZ) on eccentricity: (1) the mean-stellar ux approximation (SIHZ / p 1 􀀀 e2), in which the temperature is approximately constant throughout the orbit, and (2) the maximum-stellar ux approximation (SIHZ / (1 􀀀 e)2), in which the temperature adjusts instantaneously to the stellar ux. Which limit is appropriate is determined by the dimensionless parameter   = C BP , where C is the heat capacity of the planet, P is the orbital period, and B = @ @Ts , where is the outgoing longwave radiation and Ts is the surface temperature. We use the Buckingham   theorem to derive an analytical function for the IHZ in terms of eccentricity and  . We then build a time-dependent energy balance model to resolve the surface temperature evolution and constrain our analytical result. We  nd that   must be greater than about   1 for the mean-stellar ux approximation to be nearly exact and less than about   0:01 for the maximum-stellar ux approximation to be nearly exact. In addition to assuming a constant heat capacity, we also consider the e ective heat capacity including latent heat (evaporation and precipitation). We  nd that for planets with an Earth-like ocean, the IHZ should follow the mean-stellar ux limit for all eccentricities. This work will aid in the prioritization of potentially habitable exoplanets with non-zero eccentricity for follow-up characterization.