Mean Motion Resonances and Planetary Scattering

Abstract

The observed distribution of giant exoplanet eccentricities and inclinations are significantly
larger than what is measured for their Solar system analogues, Jupiter and Saturn.
Since the first observations of exoplanets, planet-planet scattering has been proposed as
a possible mechanism for exciting the eccentricities and inclinations of giant exoplanets.
Many works have showed that indeed the observations can be reproduced fairly well by
unstable planetary systems undergoing planet-planet scattering, e.g. Marzari & Weidenschilling
(2002); Juri´c & Tremaine (2008); Chatterjee et al. (2008). Most of these works
disregard mean motion resonances in their simulations.
In the early stages of a planet system the planets are embedded in a protoplanetary
disk, consisting mostly of gas. Planet-disk interactions causes planets to migrate which
allows for capture into mean motion resonances. This significantly affects the dynamical
evolution of the system. In this work I investigate what effect mean motion resonances
has specifically on the planet-planet scattering phase of an unstable system. I numerically
simulate systems of three Jupiter-mass planets orbiting a solar mass star, including planetdisk
interactions to form resonant configurations. The systems are split into two sets: mmr
simulations, with all planets locked in mean motion resonance chains before the scattering
phase, and non-mmr simulations, with similar initial orbital elements but no mean motion
resonances before the scattering phase.
I find that eccentricity and inclination distributions of relaxed systems are not directly
correlated with initial mean motion resonances. Resonances seem to be broken in the first
few close encounters and have no further impact on the systems afterwards. However, mean
motion resonances have an impact on the initial eccentricity, inclination and semimajor axis
of the scattering phase, all of which affects the relaxed systems. Therefore mean motion
resonances do affect the scattering phase indirectly through the initial orbital elements. The
duration of the scattering phase seems to be uncorrelated with both initial resonance and
initial eccentricity and inclination. The onset time of the scattering phase is, in contrast,
very dependent on both initial mean motion resonance and initial orbital elements.

Popular Abstract (Swedish)

Vetenskap inom planetformation a ̈r ett omr ̊ade som har utvecklats mycket sedan de allra fo ̈rsta exoplaneterna uppt ̈acktes. Da ̈r vi tidigare hade ett enda exemplar av planetsystem att studera (v ̊art egna Solsystem) har vi idag tusentals observationer av planetsystem runt andra stj ̈arnor. N ̊agot som f ̈orbryllade forskare d ̊a de fo ̈rsta uppt ̈ackterna gjordes ̈ar att exoplaneter, specifikt gasj ̈attar, har betydligt ho ̈gre excentricitet och inklination a ̈n gas ja ̈ttarna Jupiter och Saturnus i v ̊art Solsystem. Fo ̈r att beskriva denna avvikelse f ̈oreslogs teorin planet-planet spridning (planet-planet scattering). Teorin g ̊ar ut p ̊a att planeter under ett tidigt stadie kommer tillra ̈ckligt na ̈ra varandra fo ̈r att interagera kraftigt genom gravitation. Med andra ord s ̊a blir gravitationskraften mellan de tv ̊a planeterna betydlig i ja ̈mf ̈orelse med gravitationskraften fr ̊an den centrala stj ̈arnan. Under s ̊adana interaktioner kan de involverade planeterna avvika fr ̊an sina ursprungliga banor runt stj ̈arnan. Dessa avvikelser involverar bland annat excitation av excentricitet och inklination vilket skulle fo ̈rklara observationerna.
M ̊anga tidigare studier har gjorts inom a ̈mnet planet-planet spridning, ex. Marzari & Weidenschilling (2002); Juri ́c & Tremaine (2008); Chatterjee et al. (2008). Studierna g ̊ar ut p ̊a att ostabila planetsystem f ̊ar interagera genom planet-planet spridning tills dess att en eller flera planeter blir utsto ̈tta ur systemet. De kvarvarande planeterna bildar d ̊a ett stabilt system med f ̈orho ̈jd excentricitet och inclination. Dessa studier bortser fr ̊an reso- nanser mellan planetbanor, vilket har en stor effekt p ̊a planetdynamik. Resonanser mellan planetbanor uppkommer d ̊a planeternas omloppsperioder n ̈armar sig en enkel br ̊akdel, ex. 2:1 eller 3:2. Viktigt f ̈or det ha ̈r projektet a ̈r att resonanser mellan planetbanor kan stabilisera planetsystem som annars skulle varit ostabila.
I det h ̈ar projektet underso ̈ker jag hur stor effekt, om n ̊agon alls, som resonanser mellan planetbanor har p ̊a planet-planet spridningen i ostabila planetsystem. Jag unders ̈oker sa ̈rskillt hur excentricitet och inklination av planeter bero ̈rs.

• author: Dahlöf, Erik
• supervisor: Alexander Mustill
• organization: Lund Observatory - Undergoing reorganization; Department of Astronomy and Theoretical Physics - Undergoing reorganization
• course: ASTM31 20181
• year: 2018
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: mean motion resonance, orbit resonance, planetary dynamics, planet-planet scattering, planetary scattering, eccentricity, inclination, planet systems, disturbing force, orbit dynamics, orbital elements, planets, exoplanets, scattering phase, relaxation, dynamical instabilities, N-body, protoplanetary disk, planet migration, eccentricity damping, inclination damping, planet-disk interactions
• publication/series: Lund Observatory Examensarbeten
• report number: 2018-EXA135
• language: English
• id: 8947880
• date added to LUP: 2018-06-29 13:39:01
• date last changed: 2018-06-29 13:39:01