Extreme Exoplanets Production of Misaligned Hot Jupiters Dong Lai Cornell University Physics Colloquium, Columbia University, Feb.2, 2015
Number of planets by year of discovery 1500+ confirmed, 3000+ Kepler candidates
Transit Method Radial Velocity Method
~10% of Sun-like stars have habitable Earth-size planets Petigura et al 2014: 42000 stars->603 planets,10 in habitable zone (1-2 R e, ¼-4 Flux_e)
Surprises and Puzzles in Exoplanetary Systems
Orbital period puzzle
Kepler Compact Planetary Systems: Campante et al. 2015
Eccentricity Puzzle
Planet Radius Puzzle
Spin- Orbit Misalignment Puzzle ESO
Solar System OrientaAon of planet s orbital plane eclipac plane Sun s equator Murcury 7.005 3.38 Venus 3.394 3.86 Earth 0 7.15 Mars 1.850 5.65 Jupiter 1.303 6.09 Saturn 2.489 5.51 Uranus 0.773 6.48 Neptune 1.770 6.43 All major planets lie in the same plane (within 2 deg), which is inclinded to the Sun s equator by 7 deg.
Slide from Josh Winn
Triaud et al. 2010 WASP- 4b
How to Form Misaligned Hot Jupiters?
Giant planets are formed in protoplanetary disks (gas + dust) t < 10 Myrs R form > a few AU NASA
How to Form Misaligned Hot Jupiters? Two coupled quesdons: - - How did they migrate to < 0.05 AU? - - How did their orbits get misaligned with host star? This talk: Two mechanisms with surprising mechanics/dynamics
Disk- Driven MigraDon Goldreich & Tremaine 1979 Lin et al. 1996
PerturbaDon by a binary companion star Batygin 2012
Star-Disk-Binary Interactions DL 2014 M b star disk
Star-Disk-Binary Interactions M b S L d L b disk
Star-Disk-Binary Interactions M b S L d L b disk First just gravitaaonal interacaons (no accreaon )
Companion makes disk precess Disk behaves like a rigid body (bending waves, viscous stress, self-gravity) Ω pd 5 10 6 Mb cos θ db 2π yr M rout 3/2 a b 3 50 AU 300 AU
Disk makes the star precess Gravitational torque on rotating star (oblate) Mutual precession, but L d >>S Ω ps 5 10 5 Md 0.1M 2π cos θ sd yr 2 Ω rin rout 1 0.1 4R 50 AU where
Two limiting cases: (1) (2) Ω ps Ω pd : = θ sd constant Ω ps Ω pd : = θ sb constant
Ω pd 5 10 6 Mb cos θ db 2π yr M Ω ps 5 10 5 Md 0.1M 2π cos θ sd yr rout 3/2 a b 50 AU 300 AU 3 2 Ω rin rout 1 0.1 4R 50 AU Simple model: M d = 0.1M 1 +(t/0.5 Myrs)
Initial: θ db =5 θ sd =5 DL2014
Initial: θ db = 30 θ sd =5
Resonance Ω ps = Ω pd In the frame rotating at rate Ω pdˆlb Ω eˆl e
Initial: θ db = 60 θ sd =5
ComplicaDons: AccreDon and magnedc interacdon
Magnetic Star - Disk Interaction: Basic Picture MagneAc star
Romanova, Long, et al. 2012
Star-Disk-Binary Interactions Gravitational interactions Now include Accretion and Magnetic Torques
No accretion/magnetic Accretion/magnetic damps SL-angle Accretion/magnetic increases SL-angle DL2014
No accretion/magnetic Accretion/magnetic damps SL-angle Accretion/magnetic increases SL-angle DL2014
Summary (#1) Star- disk- binary interacdons With a binary companion, spin- disk misalignment is easily generated The key is resonance crossing AccreAon/magneAc torques affect it, but not diminish the effect primordial misalignment of stellar spin and disk
How to Form Misaligned Hot Jupiters?
How to Form Misaligned Hot Jupiters? Slow (secular) perturbaaon from a stellar companion (> 100 s Myrs) Combined effects of Lidov- Kozai oscillaaon + Adal dissipaaon
Lidov- Kozai OscillaDons planet orbital axis binary axis
Lidov-Kozai Oscillations planet orbital axis binary axis Eccentricity and inclinaaon oscillaaons induced if i > 40 degrees. If i large (85-90 degrees), get extremely large eccentriciaes (e > 0.99)
Hot Jupiter formation Holman et al. 97; Wu & Murray 03; Fabrycky & Tremaine 07; Naoz et al.12, Katz et al.12; Petrovich 14 Planet forms at ~ a few AU Companion star periodically pumps planet into high- e orbit (Lidov- Kozai) Tidal dissipaaon in planet during high- e phases causes orbital decay Combined effects can result in planets in ~ few days orbit from host star (a hot Jupiter is born!) Q: What is happening to the stellar spin axis?
Chaotic Dynamics of Stellar Spin Driven by Planets Undergoing Lidov-Kozai Oscillations With Natalia Storch, Kassandra Anderson Storch, Anderson & DL 2014, Science Storch & DL 2015, in press Anderson, Storch, DL 2015, in prep
The Stellar Spin Dance Ω s Star is spinning - anywhere from 3 to 30 days. oblate will precess M p
Spin Precession Stellar spin axis S wants to precess around planet orbital axis L. Ω ps L B S L θ sl θ lb θ sb Outer binary axis Planet orbital axis Stellar spin axis
Spin Precession Stellar spin axis S wants to precess around planet orbital axis L. But L itself is moving in two distinct ways: Ω ps L L B Ω pl Nodal precession (L precesses around binary axis L b ) Nutation (cyclic changes in inclination of L relative to L b ) S θ sl θ lb θ sb Outer binary axis Planet orbital axis Stellar spin axis
Spin Precession Q: Can S keep up with L? Ω pl Answer depends on Ω ps L L B Ω ps vs Ω pl S θ sl θ lb θ sb Outer binary axis Planet orbital axis Stellar spin axis
If Ω ps >> Ω pl : YES ( adiabaac ) N. Storch adiabaac means θ sl = constant, i.e. iniaal spin- orbit misalignment is maintained for all Ame Outer binary axis Planet orbital axis Stellar spin axis
If Ω ps << Ω pl : NO ( non- adiabaac ) Outer binary axis Planet orbital axis Stellar spin axis
If Ω ps ~ Ω pl : trans- adiabaac
If Ω ps ~ Ω pl : trans- adiabaac To answer, solve orbital evoluaon equaaons together with spin precession equaaon and see!
If Ω ps ~ Ω pl : trans- adiabaac Q: Is it really chaoac? Outer binary axis Planet orbital axis Stellar spin axis
If Ω ps ~ Ω pl : trans- adiabaac Ω ps L B S L θ sl θ lb θ sb
If Ω ps ~ Ω pl : trans- adiabaac S real δ S shadow Lyapunov Ame ~ 6 Myr
Complication & Richness Ω ps & Ω pl are strong funcaons of eccentricity (and Ame) Ω ps = 3GM p(i 3 I 1 ) 2a 3 S Ω ps0 M pω s a 3 Ω pl = Ω pl0 f(e) Ω pl0 n Mb M a cos θ sl (1 e 2 ) = Ω cos θ sl 3/2 ps0 (1 e 2 ) 3/2 a b 3 cos θ 0 lb Key parameter: = Ω pl0 Ω ps0 a9/2 M p Ω s The raao of orbital precession frequency to spin precession frequency at zero eccentricity
Outer binary axis Planet orbital axis Stellar spin axis ε decreases Physically: planet mass increases or stellar spin rate increases or semi- major axis decreases
Bifurcation Diagram Values recorded at eccentricity maxima, for 1500 LK- cycles Periodic islands in the ocean of chaos Quasi- chaoac regions in the calm sea
Bifurcation Diagram LogisAc Map: x n+1 = rx n (1 x n ) R.May (1976): Discrete Ame populaaon model
Recap: Planet can make the stellar spin axis evolve in a complex/chaoac way Depends on = Ω pl0 Ω ps0 a9/2 M p Ω s Ω pl Ω ps L B S L θ sl θ lb θ sb
Lidov-Kozai + Tidal Dissipation
Lidov-Kozai + Tidal Dissipation Recall = Ω pl0 Ω ps0 a9/2 M p Ω s As orbit decays, even if the iniaal state is in the non- adiabaac regime, it will end up adiabaac Chaos always has a chance to influence S- L angle (unless the system starts out very adiabaac)
Memory of Chaos A tiny spread in initial conditions can lead to a large spread in the final spin-orbit misalignment Initial orbital inclination θ lb =85± 0.05, with spindown
DistribuDons of the final spin- orbit angle Parameters: a b = 200 AU M * = M b = 1 M sun Stellar spin- down calibrated such that spin period = 27 days at 5 Gyr (Skumanich law) a = 1.5 AU
Uniform distribuaon of iniaal semi- major axes (a = 1.5 3.5 AU)
Solar- type star Massive Star (1.4 M sun )
Take- Home Message ChaoAc stellar spin dynamics has potenaally observable consequences (spin- orbit misalignment). Depends on planet mass, stellar rotaaon rate/history, etc. (Anderson, Storch & DL, in prep)
Origin of Spin Chaos N. Storch & DL 2015
Origin of Spin Chaos N. Storch & DL 2014 In Hamiltonian system, Chaos arises from overlapping resonances (Chirikov criterion; 1979)
Origin of Spin Chaos N. Storch & DL 2014 In Hamiltonian system, Chaos arises from overlapping resonances (Chirikov criterion; 1979) Ω ps & Ω pl are strong funcaons of e and t ( with period P e ) Ω ps S L θ sl θ lb L B Ω pl What resonances?? θ sb
Hamiltonian PerturbaDon Theory Spin precession Orbit s nodal precession Orbit s nutaaon
Spin- Orbit Resonances Ω ps = ᾱ cos θ sl = N 2π P e Average spin precession frequency = Integer mulaple of mean Lidov- Kozai frequency
Individual Resonance N=0
Individual Resonance
MulDple Resonances Together CondiAon for chaos: resonance overlap
Poincare Surface of SecDon (Full System)
Poincare Surface of SecDon (Full System)
Boundary of ChaoDc Zone AnalyAcal theory: From outmost overlapping resonances
Numerical BifurcaDon Diagram StarAng from zero spin- orbit angle
Summary Many exoplanetary systems are quite different from the Solar syetem FormaDon of misaligned Hot Jupiters: (1) Disk driven migradon Star- disk- binary interacaons primordial misalignment between star and disk (2) Lidov- Kozai oscilladons + Dde high- e migradon chaoac dynamics of stellar spin during LK cycles: - - important for the observed spin- orbit misalignments, depend on planet mass, stellar rotaton/history etc. - - Spin dynamics can be understood from resonance theory
Thanks!
Is High-e Migration the whole story for producing hot Jupiters and S-L misalignments? Likely NOT. -- Companion? Initial conditions? (e.g., Knutson et al. 2014) -- Paucity of high-e proto-hot Jupiters (Socrates et al.2012; Dawson et al.2012) -- Stellar metallicity trend of hot Jupiters Two mechanisms of migrations (Dawson & Murray-Clay 2013) -- Misaligned multiplanet systems: Kepler-56 (2 planets 10.5 & 21 days 40-55 deg from seismology; Huber et al 2013) Kepler-25 (2 transiting planets, one non-transiting; Benomar et al 2014) 55 Cancri (?? Bourrier & Hebrard 2014; Lopez-Morales et al. 2014) Other Candidates: Hirano et al. 2014; Kepler-9 (?? Walkowicz & Basri 2013) See Boue & Fabrycky 2014
Hints of Primordial Misalignments (before dynamical few- body interacaons) - - Solar system: 7 degree - - Stellar spin axes in a>40 AU binaries: Misaligned (Hale 1994) - - PMS/YSO binaries: Misaligned protostellar disks measured from jets or disks Haro 6-10: Two disks: one edge- on, one face- on (Roccatagliata et al. 2011)
Ideas for Producing Primordial Misalignments between Stellar Spin and Protoplanetary Disk -- Chaotic star formation (Bate et al. 2010; Fielding et al.2014) -- Magnetic Star Disk Interaction (Lai, Foucart & Lin 2011) -- Perturbation of Binary on Disk (Batygin 2012; Batygin & Adams 2013; DL 2014)
Recap the Key Findings: -- With a binary companion, spin-disk misalignment is easily generated -- Accretion/magnetic torques affect it, but not diminish the effect -- The key is resonance crossing
Implications for Hot Jupiter formation -- If hot Jupiters are formed through Kozai induced by a companion, then primordial misalignment likely already present -- Even when Kozai is suppressed, misaligned planets can be produced -- Disk driven migration is quite viable
S*- L p misalignment in Exoplanetary Systems The Importance of few- body interacdons 1. Planet- planet InteracAons - - Strong sca erings (e.g., Rasio & Ford 96; Cha erjee et al. 08; Juric & Tremaine 08) - - Secular interacaons/chaos (e.g Nagasawa et al. 08; Wu & Lithwick 11) 2. Lidov- Kozai oscillaaons induced by a distant companion star/planet (e.g., Holman et al. 97; Wu & Murray 03; Fabrycky & Tremaine 07; Naoz et al.12, Katz et al.12; Petrovich 14)
High- Order Lidov- Kozai Effects: Liu, Munoz & DL 2015
Boundary of ChaoDc Zone From outermost overlapping resonance
Summary (# 2) Dynamics of stellar spin is important for the observed spin- orbit misalignments in hot Jupiter systems (dependence on planet mass, stellar rotaton/history etc) Spin dynamics can be chaoac Spin dynamics can be understood from resonance theory