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Timing of Transiting Planets Eric Agol, University of Washington

Timing of Transiting Planets Eric Agol, University of Washington. Three exoplanet problems:. Migration : Do Jupiters capture earths into (near) mean-motion resonance? Inclination : RV measures M * sin(I) I for non-transiting planets?

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Timing of Transiting Planets Eric Agol, University of Washington

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  1. Timing of Transiting PlanetsEric Agol, University of Washington

  2. Three exoplanet problems: • Migration: Do Jupiters capture earths into (near) mean-motion resonance? • Inclination: RV measures M*sin(I) • I for non-transiting planets? • relative inclination of multi-planet systems? scattering vs. disk interaction • Planet structure: high precision radius/mass measurements (cf. Guillot, LeConte, Valencia)

  3. A solution: transit timing • A single planet follows Keplerian orbit - transit evenly spaced • A second planet will perturb the orbit of the first, causing a change in the times between transit (Miralda-Escudé 2002, Agol, Steffen, Sari & Clarkson 2005, Holman & Murray 2005) • On short timescales, months-years, can be significant , possibly measurable with CoRoT (if lucky)

  4. tM Relative flux tI tI Time Slide credit: Josh Winn

  5. Relative flux DF = (Rp/R*)2 t2 t1 P Time Slide credit: Josh Winn

  6. Transit Timing Variations (TTV) Best-Fit Periodic Orbit minus Time Time Transit Number Transit Number Timing Residuals Time Transit Number Transit Time

  7. 1) Short period resonant earths? Librating resonant planets: Need observations spaced over  months with  seconds precision - in principle sensitive to  Mars mass (Agol et al. 2005)

  8. Timing precision • Proportional to the photometric precision, exp • Fisher matrix analysis (Carter 2008, Ford & Gaudi 2007): • This is not always achieved in practice due to correlated noise, stellar variability, spots, etc... • Best precisions obtained are ~5 seconds from the ground (VLT & Magellan: Gillon et al. 2008; Winn et al. 2009); ~3-5 seconds with Spitzer/HST (Knutson et al. 2007; Pont et al. 2008; Agol et al. 2008) • Best CoRoT timing precision is 5 seconds for CoRoT-Exo-1b; Poster P-VIII-83, Csizmadia

  9. TTV Analysis TTV Theory (1) TTV + RV (2) RV Theory (3) HST TTV & RV for HD 209458 Maximum allowed mass for companion on initially circular orbit Also: HD 189733 (Pont et al. 2007)

  10. Transit Timing Observation Summary • Transit Light Curve (TLC) Project (Winn & Holman, PIs, 12+ papers) - achieve 5-50 sec precision • CoRoT Exo-1-b, Exo-5-b: Posters P-V-51, Rauer; P-V-50, Fridlund; P-VIII-83, Csizmadia • Jena telescope: Poster P-XIII-121, Raetz - XO-1b, Tres-1, Tres-2 • MOST: Miller-Ricci et al. (2008) HD 189733, 209458 • GJ 436c? Alonso et al. (2009) • EPOXI: Christensen et al. (2008) • Spitzer: Agol et al. (2008) • VLT: OGLE-111b - Diaz et al. (2008) Rien Rien Rien Rien Rien Rien Rien Probablement rien

  11. 2) Constraining absolute mass/radius: case study of GJ 876 • Super-Earth (2 day) + 2 Jupiters (30, 60 days) orbiting M- dwarf (0.3M) Rivera et al. 2005 • Pretend orbits align & transit (p~0.7%)

  12. GJ 876 TTV: Libration ~600 days

  13. GJ 876b,c,d: measuring mass/radius • Light curve constructed for 600 days with 10-3 day exposures (84 sec) from 26 parameters: M/R of star & planets (8), orbital elements of planets (18). • Fisher matrix analysis gives an estimate of uncertainties vs. photometric errors (Carter 2008) • Find fractional uncertainties on GJ 876d (7.5 M) mass of 510-4 and radius of 610-4 (without radial velocity) for 1 mmag (assume stellar variability can be filtered) • Try putting that on a Toblerone diagram!

  14. 3) Constraining inclination: case study of HIP 14810b,c • Hot Jupiter, 6.6742 days, plus longer period eccentric Jupiter, 95 days, e  0.4 • Both are detected with RV; if inner planet were to transit, we would know its inclination • If outer planet does not transit, it would have an uncertain inclination (I) & orientation on sky () • Non-transiting planet has mass Msin(I), so I affects the perturbations of inner planet due to changing mass & relative inclination

  15. HIP 14810c: constraining inclination with TTV

  16. Additional effects • Exo-moons (Poster P-VIII-89: David Kipping) • Trojans - offset in radial velocity & transit time (Poster P-III-33: Moldovan; P-III-34: Dvorak; Ford & Gaudi 2006; Ford & Holman 2007) • Relativistic effects - precession of orbit (e.g. Miralda-Escudé 2002, Loeb 2005, Heyl & Gladman 2007, Pál & Koscis 2008, Jordán & Bakos 2008) • Light-travel time - requires large planet mass & large semi-major axis (Poster P-VIII-86, Cabrera) • Transit parallax (Scharf 2007) - very small • Tidal evolution (Ragazzine & Wolf 2009)

  17. Conclusions • No convincing evidence yet for planet-induced TTV - maybe resonant terrestrial planets aren’t there or need longer time baseline & higher precision. • In principle can constrain inclination of non-transiting planets, and mass/radius if both transit. • CoRoT drawbacks: 1) duration may not be long enough; 2) low-Earth orbit limits photometric precision, which limits transit timing precision; 3) stars are fainter & variable. • CoRoT advantages: 1) measuring a large number of transits for each; 3) best possibility of finding multi-planet transiting systems; 4) longer period planets (Exo-4b,6b): larger TTV

  18. Extra slides

  19. Four observables, four derivables: • Flux decrement F • Transit duration tM • Ingress duration tI • Period P=t2-t1 • b/R*=[1-tMF1/2/tI]1/2 • Rp/R* = F1/2 • a/R* = P/tM • * = 3P/(GtM3) • With velocity semi-amplitude, K, can also derive surface gravity of planet • Can look for variations in each of these parameters - transit times are best b=0 Seager& Mallen-Ornelas 2003 Winn et al. (2007); Southworth et al. (2007); Beatty et al. (2007); Sozzetti et al. (2007)

  20. 28 Multi-planet RV systems (Wright et al. 2009). I’ll discuss two case studies which have a reasonable probability of transit.

  21. Earth/Super-Earth mean-motion TTV TTV for an Earth-mass planet in 2:1 mean-motion resonance - amplitude is 200 seconds - mass sensitivity scales as Mtrans1/2

  22. TTV induced by exterior eccentric planet (non-resonant) Changing proximity to inner binary alters the tidal force on inner binary. Agol et al. (2005)

  23. 1. Do (near-)resonant short period systems exist? Zhou et al. 2005 • During migration of giant planets, terrestrial-mass cores can caught in or near low order mean-motion resonances (Narayan et al. 2004; Mandell & Sigurdsson 2004; Thommes 2005, Mandell & Raymond 2007) • Can these survive for Gyr timescales? (1011 dynamical times) 2:1 Terquem & Papaloizou (2006) 3:2

  24. Probability of multi-planet transits Fabrycky (2008) • I  5o • Ptransit ain/aout • N =  Ptransit = 1.7 (<100 d)

  25. HIP 14810c: constraining Omega with TTV

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