Inner Habitable Zone Boundary for Eccentric Exoplanets

The climate of a planet can be strongly affected by its eccentricity due to variations in the stellar flux. There are two limits for dependence inner habitable zone boundary (IHZ) on eccentricity: (1) mean-stellar flux approximation ($S_{\mbox{IHZ}} \propto \sqrt{1-e^2}$), which temperature is approximately constant throughout orbit, and (2) maximum-stellar (1-e)^2$), adjusts instantaneously Which limit appropriate determined dimensionless parameter $\Pi = \frac{C}{BP}$, where $C$ heat capacity planet, $P$ orbital period, $B=\frac{\partial \Omega}{\partial T_s}$, $\Omega$ outgoing longwave radiation $T_s$ surface temperature. We use Buckingham $\Pi$ theorem derive an analytical function IHZ terms $\Pi$. then build time-dependent energy balance model resolve evolution constrain our result. find that must greater than about $\sim 1$ nearly exact less 0.01$ exact. In addition assuming capacity, we also consider effective including latent (evaporation precipitation). planets with Earth-like ocean, should follow all eccentricities. This work will aid prioritization potentially exoplanets non-zero follow-up characterization.