# DDA 2015 – Obliquity Evolution of Earth-Like Exoplanets in Systems with Large Inclinations

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Russell Deitrick (U. Washington)

#### Abstract

In order to properly assess the potential for habitability and prioritize target selection for the characterization of exoplanets, we need to understand the limits of orbital and rotational dynamics. Large satellites may be rare and very difficult to detect. Consequently, it is necessary to quantify the likelihood of a planet’s having extreme obliquity cycles in the absence of a moon and to model the potential impact on the planet’s climate. We explore the obliquity evolution of (1) known exoplanet systems that could contain Earth-like planets in the habitable zone and (2) hypothetical planets in mutually inclined, chaotic resonant configurations that experience some of the most extreme orbital evolution possible. We use a secular obliquity model coupled to either an N-body models or a 4 order secular orbital model. We find that in some known systems, planets’ obliquity variations are small and unlikely to have a major effect on climate, unless undetected planets are present. Systems with three or more planets are significantly more dynamically rich, with planets that undergo obliquity changes of ~10° over 50,000 years and >30° over a few million years. In resonant configurations, Earth-like exoplanets can undergo dramatic and chaotic evolution in eccentricity and inclination while remaining stable for over 10 Gyr. In configurations in which eccentricities and inclinations stay below ~0.1 and~10°, respectively, obliquities oscillate quasi-periodically with amplitudes similar to the non-resonant, three-planet configurations. In more dynamically active configurations, in which eccentricities and inclinations evolve to e > 0.3 and i > 15°, obliquities can extend from ~0° to well past 90°. In extreme cases eccentricities can reach >0.9999 and inclinations >179.9 degrees, driving precession rates in excess of degrees per year. However, these planets can graze or impact the stellar surface and are probably not habitable.

#### Notes

• $\upsilon$Andromedae c and d
• obliquity oscillations
• Model description
• Barnes, Deitrick et al. 2015
• Using the secular disturbing function (Murray & Dermott) and a secular obliquity model (Kinoshita 1975, 1977)
• HD190360
• obliquity varies w large amplitude in a “strip” in $\Delta i_0$ – $e_0$ plane — WTH?
• two planets interacting (an Earth and a super-Jupiter) … somehow
• Inside the “strip”, a commensurabilitylibrates
• $(\varpi’ – \varpi) – (\Omega + p_A)$
• outside the “strip”: no libration
• Analogous to a compound pendulum
• Summary
• Non-coplanar systems in MMR exhibit long-lived chaos.
• These systems can be formed by scattering.
• Possible way to form misaligned hot Jupiters.
• Earth-like planets in these systems can also have chaotic obliquity variations.