The eccentric behavior of planets

Transcription

1 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

2 Effects on planetary architecture with or without? Not to scale!

3 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!!

4 Effects on planetary architecture Hierarchical triple system with? Not to scale!

5 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

6 The Kozai-Lidov Formalism The eccentricity and inclination oscillate Kozai 1962, Lidov 1962 For initially inclined system 40 o

7 The Kozai-Lidov Formalism The eccentricity and inclination oscillate Kozai 1962, Lidov 1962 For initially inclined system 40 o

8 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: Naoz et al (2013),MNRAS, arxiv:

9 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 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: Naoz et al (2013), MNRAS, arxiv: i>90 deg - retrograde for test particle approx. see: Lithwick & Naoz (2011), ApJ, arxiv: Katz, Dong Malhotra (2011), arxiv: ??

10 Lets...flip the planet

11 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)

12 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)

13 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

14 Secular evolution in planetary systemslong Time Scale Planets architecture: eccentricities, obliquities, long term stability etc smash the mass

15 Planets are eccentric exoplanets.org 9/24/ Orbital Eccentricity Semi-Major Axis [Astronomical Units (AU)]