## DDA 2015 – Consolidating and Crushing Exoplanet Systems

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.

Kathryn Volk (U. British Columbia)

#### Abstract

Kepler revealed the common existence of tightly-packed planetary systems around solar-type stars, existing entirely on orbits with periods shorter than ~200 days. Those systems must have survived for the ages of their host stars (~5 Gyr), so their formation mechanism must provide inter-planet spacings that permit long-term stability. If one postulates that most planetary systems form with tightly-packed inner planets, their current absence in some systems could be explained by the collisional destruction of the inner system after a period of meta-stability. The signatures of such intense collisional environments may have been observed around stars in the form of rapidly varying debris disks; in these observed disks, collisional products are being disposed of via drag down onto the star or grinding to the nearly instantaneous dust blow-out limit. We use the orbital spacings and planet masses of the observed Kepler multi-planet systems to investigate the stability and long-term behavior of the systems. We find that many of our Kepler system analogs are unstable on 100 Myr timescales, even for initially small eccentricities (0-0.05); the instability timescales in these systems are distributed such that equal fractions of the systems experience planetary collisions in each decade in time. We discuss the likely outcomes of collisions in these systems based on the typical collision speeds from our numerical integrations and what implications this has for interpreting the observed Kepler multi-planet systems. The possible implications for our Solar System are discussed in a companion abstract (Gladman and Volk).

#### Notes

• Architectures of close-in (closely packed) planetary systems (from Kepler)
• Fabrycky 2014
• ~5-10% ofFGK field stars
• These systems must be stable on Gyr timescales
• Are all stars formed tightly packed?
• Modeled 13 such Kepler systems
• Preserved $a$ and masses, orbital angles randomized
• Allowed $e_0$ to vary $0 < e_0 < 0.05$
• Sudden onset of instability in 11 of these 13 after tens to ~100 Myr
• [why is she surprised?]
• These eccentricities are in range of observed values
• Decay rates consistent with e.g. Holman & Wisdom (1992 AJ)
• Why sudden onset?
• History is very sensitive to ICs [duh]
• Consolidation (low-speed collisions) vs. Destruction (high-speed collisions)
• First collision is often near the accretion/erosion boundary — i.e., low-speed
• Masses in 4-5 planet systems tend to be lower, while individual masses in ~3-planet systems are higher: mergers?
• Tracked collision speeds during integrations.
• Second collision often goes into erosion regime (i.e., high-speed)
• Observing debris should be rare (but see Meng et al. 2012)
• Ergodicity allows large variety of outcomes
• $\Rightarrow$ tightly packed systems could be ubiquitous initially
• Young stars should show higher fraction
• The remaining ~95% should be 0-2 planet systems

## DDA 2015 – Capture into Mean-Motion Resonances for Exoplanetary Systems

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 II

Maryame El Moutamid (Cornell)

#### Abstract

Many bodies in the Solar System and some exo-planets are close to or captured in Mean Motion Resonances (MMR). Capture into such resonances has been investigated by many authors. Indeed, the Hamiltonian equations of motion in presence of migration are given by Sicardy and Dubois Cel. Mech. & Dyn. Astron., 86, 321-350 (2003). Fleming and Hamilton, Icarus 148, 479-493 (2000), studied the problem in a less generic context. In these two papers, the authors studied the problem of 1:1 corotation (Lagrange points L4 and L5), rather than m+1:m corotations (El Moutamid et al, Cel. Mech. & Dyn. Astron, 118, 235-252 (2014)). We will present a generic way to analyze details of a successful (or not) capture in the case of an oblate (or not) central body in the context of Restricted Three Body Problem (RTBP) and a more General Three Body Problem in the context of known statistics for captured exoplanets (candidates) observed by Kepler.

#### Notes

• Captures partial near MMR (Fabrycky et al. 2012)
• No generic study on coupling between associated resonances (ERTB vs. general TB)
• 1) simple model,2DoF — $(m+1) n’ \approx m n$
• splitting the corotation and Lindblad resonances (by $J_2 \neq 0$)
• Lindblad: vary $e$
• corotation: pendular motion (conserves $e$)
• plot: $J_c – J_L$ vs. $\phi_C$
• 2) general case
• can define a constant of motion: $J_{c,relat} = \frac{A^2 \xi}{m} – \frac{A’^2 e’}{m+1} – ?? = const.$
• ratio: potential barrier of one vs. other body
• plot: potential energy vs. critical angle of corotation
• probability of capture: very very small

## 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?