The eccentric behavior of planets (and their eccentric companions) Smadar Naoz UCLA! ExSoCal2015 September 2015 Collaborators: (current students:) Alexander Stephan, Bao-Minh Hoang, Cicero Lu, (former students:) Jean Teyssandier,Gongjie Li, Will Farr, Yoram Lithwick, Fred Rasio, Avi Loeb, Bence Kocsis, Matt Holman, John Johnson
Effects on planetary architecture with or without? Not to scale!
Q: What are the different physical processes that affect planets? Interactions with protoplanetary disk Planet-Planet scattering Perturbations by another object credit: Gongjie Li credit: Fred Rasio companion And much more!!
Effects on planetary architecture Hierarchical triple system with? Not to scale!
The Kozai-Lidov Formalism Hierarchical triple system Not to scale! Kozai 1962, Lidov 1962 Orbit normal inner outer Orbit normal i inclination? smash the mass
The Kozai-Lidov Formalism The eccentricity and inclination oscillate Kozai 1962, Lidov 1962 For initially inclined system 40 o
The Kozai-Lidov Formalism The eccentricity and inclination oscillate Kozai 1962, Lidov 1962 For initially inclined system 40 o
The Kozai-Lidov Formalism EKL The eccentricity and inclination oscillate Kozai 1962, Lidov 1962 Conservation of the z component of angular momentum for both the inner outer orbits The orbital elements: previous treatments, Eccentricity: e Lz~ 1 e2 cos i = const) Inclination: i L z1 conserved only to lowest order Prograde orbit cannot become (quadrupole) and retrograde for a test particle (massless planet)! Naoz et al, Nature (2011), arxiv:1011.2501 Naoz et al (2013),MNRAS, arxiv:1107.2414
Our treatment The eccentric Kozai-Lidov mechanism - EKL Allow for the z-component of the angular momenta of the inner and outer orbit to change - already at the quadrupole level i<90 deg - prograde Expanding the approximation to the octupole level (e.g., Ford et al 2000, Blaes et al 2002 - already done before us!!!) Both the magnitude and orientation of the angular momentum can change larger parts of the parameter space Naoz et al, Nature (2011), arxiv:1011.2501 Naoz et al (2013), MNRAS, arxiv:1107.2414 i>90 deg - retrograde for test particle approx. see: Lithwick & Naoz (2011), ApJ, arxiv:1106.3329 Katz, Dong Malhotra (2011), arxiv:1106.3340??
Lets...flip the planet
point mass limit Lets...flip the planet Example system: a1=6au, a2=100au, m1=1.msun M2=1Mj, M3=40Mj i=65 deg secular dynamics + GR GR effects: e.g., Ford et al 2000, Naoz, Kocsis, Loeb, Yunes 2013 (a) inner orbit inclination (b) inner orbit eccentricity circular eccentric (c) inner orbit z-com. angular momentum (d) inner orbit z-com. angular momentum Naoz et al, Nature (2011)
point mass limit Lets...flip the planet Example system: a1=6au, a2=100au, m1=1.msun M2=1Mj, M3=40Mj i=65 deg secular dynamics + GR GR effects: e.g., Ford et al 2000, Naoz, Kocsis, Loeb, Yunes 2013 (a) inner orbit inclination (b) inner orbit eccentricity (c) inner orbit z-com. angular momentum Compare to: Standard (quadrupole) Kozai (d) inner orbit z-com. angular momentum Naoz et al, Nature (2011)
EKL + Tides + spin-orbit angle The system: a1=6au a2=61au m1=1 Msun, m2=1 Mj, m3=3mj i=71.5 (a) inner orbit inclination (b) inner orbit eccentricity (c)sma and separations (a) (b) Tides follow - Eggleton, Kiseleva & Hut 1998, Fabrycky & Tremaine (2007) (c) Naoz et al, Nature, 2011
Secular evolution in planetary systemslong Time Scale Planets architecture: eccentricities, obliquities, long term stability etc smash the mass
Planets are eccentric exoplanets.org 9/24/2015 0.8 Orbital Eccentricity 0.6 0.4 0.2 0.0 0.1 1 10 Semi-Major Axis [Astronomical Units (AU)]