## 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.

## DDA 2015 – Loners, Groupies, and Long-term Eccentricity Behavior – Insights from Secular Theory

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.

Christa Van Laerhoven (CITA)

#### Abstract

Considering the secular dynamics of multi-planet systems provides substantial insight into the interactions between planets in those systems. Secular interactions are those that don’t involve knowing where a planet is along its orbit, and they dominate when planets are not involved in mean motion resonances. These interactions exchange angular momentum among the planets, evolving their eccentricities and inclinations. To second order in the planets’ eccentricities and inclinations, the eccentricity and inclination perturbations are decoupled. Given the right variable choice, the relevant differential equations are linear and thus the eccentricity and inclination behaviors can be described as a sum of eigenmodes. Since the underlying structure of the secular eigenmodes can be calculated using only the planets’ masses and semi-major axes, one can elucidate the eccentricity and inclination behavior of planets in exoplanet systems even without knowing the planets’ current eccentricities and inclinations. I have calculated both the eccentricity and inclination secular eigenmodes for the population of known multi-planet systems whose planets have well determined masses and periods. Using this catalog of secular character, I will discuss the prevalence of dynamically grouped planets (‘groupies’) versus dynamically uncoupled planets (‘loners’) and how this relates to the exoplanets ‘long-term eccentricity and inclination behavior. I will also touch on the distribution of the secular eigenfreqiencies.

#### Notes

• Secular character of multi-planet system
• planet-planet interactions
• only need masses and semimajor axes (not eccentricity, not inclination) to set secular structure
• two-planet system: two eccentricityeigenmodes
• $h = e \sin \varpi$, $k = e \cos \varpi$ plot: $e$ is a vector
• each $e$ vector is the sum of two eigenvectors
• 3-planet system: “groupie”-ness and loners
• groupies:
• $e$ highly variable
• $\varpi$ precession not uniform
• loners:
• $e$ does not vary by much
• $\varpi$ precesses steadily
• Kepler-11
• outer planet is a loner — does not interact with others
• 5 inner planets are groupies — interact strongly with each other
• Summary: most planets are “groupies”, “loners” are rare.

## DDA 2015 – Using Populations of Gas Giants to Probe the Dynamics of Planet Formation

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.

### Session: Exoplanet Theory I

Ruth Murray-Clay (UC Santa Barbara) (invited)

[none]

#### Notes

• How do giant planets and brown dwarfs form?
• Architecture of Solar System is atypical.
• Lots of gas giants at large distances, small distances (“hot Jupiters”), but not much in between a la Solar System. Why?
• SS: rocky planets (~1 AU), gas giants (~5-10 AU), ice giants (~20-30 AU)
• Theory: cannot predict numbers, but can predict patters in system architectures and statistical populations
• How to get companions to stars: 1) turbulent fragmentation, 2) grav. instability, 3) core accretion
• HR8799: testbed for planet formation theories
• 4 Jupiter-mass planets
• turbulent frag.? No: system is not hierarchichal
• grav. inst.?
• iffy – minimum fragment distance problems (but could have migrated)
• Timing – collapse must occur at end of infall or a binary star results
• core accretion?
• dynamical (growth) timescale is too long ($t_{grow} > t_{infall}$)
• $t_{grow} > t_{disk}$
• cross section regimes — all problematic:
• physical cross section
• grav focusing
• gas drag capture
• Make gas useful.
• no gas: particles can orbit inside core Hill radius
• gas: “wind shear”
• binary capture
• particle capture can occur out to Hill radius
• growth time at 70 AU can be short enough to nucleate an atmosphere
• turbulent gas: okay
• accretion cross sections increase by up to $10^4$
• Gemini Planet Imager could confirm this theory.
• Metal-rich stars hostmorehotJupiters and highly eccentric planets: signature of planet-planet interactions? Why?
• Scattering?
• Secular chaos?
• Perhaps those systems form many Jupiters.
• Are the solar system analogs orbiting low metallicity stars?