Obliquity and Eccentricity Constraints for Terrestrial Exoplanets

Abstract

Exoplanet discoveries over recent years have shown that terrestrial planets are exceptionally common. Many of these planets are in compact systems that result in complex orbital dynamics. A key step toward determining the surface conditions of these planets is understanding the latitudinally dependent flux incident at the top of the atmosphere as a function of orbital phase. The two main properties of a planet that influence the time-dependent nature of the flux are the obliquity and orbital eccentricity of the planet. We derive the criterion for which the flux variation due to obliquity is equivalent to the flux variation due to orbital eccentricity. This equivalence is computed for both the maximum and average flux scenarios, the latter of which includes the effects of the diurnal cycle. We apply these calculations to four known multi-planet systems (GJ 163, K2-3, Kepler-186, and Proxima Centauri), where we constrain the eccentricity of terrestrial planets using orbital dynamics considerations and model the effect of obliquity on incident flux. We discuss the implications of these simulations on climate models for terrestrial planets and outline detectable signatures of planetary obliquity.

Habitable Zones in Binary Star Systems: A Zoology

“…Exoplanetary system architectures are diverse and can differ from the one of our Solar System, however. Many authors have investigated the effect of planetary eccentricity, and hence variable insolation, on potentially habitable worlds (e.g., [16][17][18][19][20][21][22][23][24][25]). In such cases the assumption of constant insolation can break down entirely.…”

“…Figure 4. A visualization of Equation(19) showing the maximum displacement of the inner (I, dashed) and outer (O, continous) border of the isophote-based habitable zone as a function of the binary orbit pericenter distance q. The displacement is given in relative to the original single star habitable zone borders.…”

HD 191939: Three Sub-Neptunes Transiting a Sun-like Star Only 54 pc Away

“…The results of the simulation indicate that the HD 191939 system is stable based on the observed orbital parameters. In addition, there is little interaction between the planets and their eccentricities remain below 0.01 for the duration of the simulation, resulting in minimal impact on insolation flux received by the planets that would affect climate (Kane & Torres 2017). In particular, the innermost planet retains a circular orbit since it is the most massive and primarily influenced by the host star.…”

GJ 273: on the formation, dynamical evolution, and habitability of a planetary system hosted by an M dwarf at 3.75 parsec

“…Spiegel et al 2009;Armstrong et al 2014;Shields et al 2016b). In the work by Kane & Torres (2017), the authors described the maximum flux received by a planet as a function of the latitude, β, the orbital eccentricity, the orbital phase, φ, and the obliquity, , as follows:…”