Extreme Exoplanets Production of Misaligned Hot Jupiters. Dong Lai Cornell University

Transcription

1 Extreme Exoplanets Production of Misaligned Hot Jupiters Dong Lai Cornell University Physics Colloquium, Columbia University, Feb.2, 2015

2 Number of planets by year of discovery confirmed, Kepler candidates

3 Transit Method Radial Velocity Method

4 ~10% of Sun-like stars have habitable Earth-size planets Petigura et al 2014: stars->603 planets,10 in habitable zone (1-2 R e, ¼-4 Flux_e)

5 Surprises and Puzzles in Exoplanetary Systems

6 Orbital period puzzle

7 Kepler Compact Planetary Systems: Campante et al. 2015

8 Eccentricity Puzzle

9 Planet Radius Puzzle

10 Spin- Orbit Misalignment Puzzle ESO

11 Solar System OrientaAon of planet s orbital plane eclipac plane Sun s equator Murcury Venus Earth Mars Jupiter Saturn Uranus Neptune All major planets lie in the same plane (within 2 deg), which is inclinded to the Sun s equator by 7 deg.

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13 Slide from Josh Winn

14 Triaud et al WASP- 4b

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16 How to Form Misaligned Hot Jupiters?

17 Giant planets are formed in protoplanetary disks (gas + dust) t < 10 Myrs R form > a few AU NASA

18 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

19 Disk- Driven MigraDon Goldreich & Tremaine 1979 Lin et al. 1996

20 PerturbaDon by a binary companion star Batygin 2012

21 Star-Disk-Binary Interactions DL 2014 M b star disk

22 Star-Disk-Binary Interactions M b S L d L b disk

23 Star-Disk-Binary Interactions M b S L d L b disk First just gravitaaonal interacaons (no accreaon )

24 Companion makes disk precess Disk behaves like a rigid body (bending waves, viscous stress, self-gravity) Ω pd Mb cos θ db 2π yr M rout 3/2 a b 3 50 AU 300 AU

25 Disk makes the star precess Gravitational torque on rotating star (oblate) Mutual precession, but L d >>S Ω ps Md 0.1M 2π cos θ sd yr 2 Ω rin rout R 50 AU where

26 Two limiting cases: (1) (2) Ω ps Ω pd : = θ sd constant Ω ps Ω pd : = θ sb constant

27 Ω pd Mb cos θ db 2π yr M Ω ps Md 0.1M 2π cos θ sd yr rout 3/2 a b 50 AU 300 AU 3 2 Ω rin rout R 50 AU Simple model: M d = 0.1M 1 +(t/0.5 Myrs)

28 Initial: θ db =5 θ sd =5 DL2014

29 Initial: θ db = 30 θ sd =5

30 Resonance Ω ps = Ω pd In the frame rotating at rate Ω pdˆlb Ω eˆl e

31 Initial: θ db = 60 θ sd =5

32 ComplicaDons: AccreDon and magnedc interacdon

33 Magnetic Star - Disk Interaction: Basic Picture MagneAc star

34 Romanova, Long, et al. 2012

35 Star-Disk-Binary Interactions Gravitational interactions Now include Accretion and Magnetic Torques

36 No accretion/magnetic Accretion/magnetic damps SL-angle Accretion/magnetic increases SL-angle DL2014

37 No accretion/magnetic Accretion/magnetic damps SL-angle Accretion/magnetic increases SL-angle DL2014

38 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

39 How to Form Misaligned Hot Jupiters?

40 How to Form Misaligned Hot Jupiters? Slow (secular) perturbaaon from a stellar companion (> 100 s Myrs) Combined effects of Lidov- Kozai oscillaaon + Adal dissipaaon

41 Lidov- Kozai OscillaDons planet orbital axis binary axis

42 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)

43 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?

44 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

45 The Stellar Spin Dance Ω s Star is spinning - anywhere from 3 to 30 days. oblate will precess M p

46 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

47 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

48 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

49 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

50 If Ω ps << Ω pl : NO ( non- adiabaac ) Outer binary axis Planet orbital axis Stellar spin axis

51 If Ω ps ~ Ω pl : trans- adiabaac

52 If Ω ps ~ Ω pl : trans- adiabaac To answer, solve orbital evoluaon equaaons together with spin precession equaaon and see!

53 If Ω ps ~ Ω pl : trans- adiabaac Q: Is it really chaoac? Outer binary axis Planet orbital axis Stellar spin axis

54 If Ω ps ~ Ω pl : trans- adiabaac Ω ps L B S L θ sl θ lb θ sb

55 If Ω ps ~ Ω pl : trans- adiabaac S real δ S shadow Lyapunov Ame ~ 6 Myr

56 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

57 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

58 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

59 Bifurcation Diagram LogisAc Map: x n+1 = rx n (1 x n ) R.May (1976): Discrete Ame populaaon model

60 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

61 Lidov-Kozai + Tidal Dissipation

62 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)

63 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

64 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

65 Uniform distribuaon of iniaal semi- major axes (a = AU)

66 Solar- type star Massive Star (1.4 M sun )

67 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)

68 Origin of Spin Chaos N. Storch & DL 2015

69 Origin of Spin Chaos N. Storch & DL 2014 In Hamiltonian system, Chaos arises from overlapping resonances (Chirikov criterion; 1979)

70 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

71 Hamiltonian PerturbaDon Theory Spin precession Orbit s nodal precession Orbit s nutaaon

72 Spin- Orbit Resonances Ω ps = ᾱ cos θ sl = N 2π P e Average spin precession frequency = Integer mulaple of mean Lidov- Kozai frequency

73 Individual Resonance N=0

74 Individual Resonance

75 MulDple Resonances Together CondiAon for chaos: resonance overlap

76 Poincare Surface of SecDon (Full System)

77 Poincare Surface of SecDon (Full System)

78 Boundary of ChaoDc Zone AnalyAcal theory: From outmost overlapping resonances

79 Numerical BifurcaDon Diagram StarAng from zero spin- orbit angle

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81 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

82 Thanks!

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84 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 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

85 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)

86 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)

87 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

88 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

89 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)

90 High- Order Lidov- Kozai Effects: Liu, Munoz & DL 2015

91 Boundary of ChaoDc Zone From outermost overlapping resonance

92 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