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This study focuses on the modeling and observation of Kepler planetary systems with significant transit timing variations (TTVs). The research aims to uncover the unique mass-radius relationships, dynamical properties, and full system architectures of these systems. By utilizing TTVs, we can enhance our understanding of resonant dynamics, migration constraints, and the potential existence of additional planets in multi-transiting systems. The study combines insights from numerous researchers to deliver comprehensive results, contributing substantially to the field of exoplanet studies.
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Modeling and Observing KeplerPlanetary Systems with Large TTVs *Sloan Fellowship Daniel Fabrycky*, Eric Agol, Kevin Stevenson, Sarah Ballard, Roberto Sanchis-Ojeda, Joshua Winn, Matthew Holman, TseviMazeh, Kepler Team and the World *U Chicago
Transit Timing Variations Agol et al. 2005, Murray & Holman 2005
The Promise Agol, Steffen, Sari, Clarkson (2005)
The Frustration TrES-2 HD 209458 Steffen & Agol 2005 Agol & Steffen 2007
The Frustration Miller-Ricci+07 HD209458 Miller-Ricci+07 HD189733 Miller-Ricci+06 HD189733 Ballard+10 GJ436 Adams+10 OGLE-TR-113 Gibson+10 TrES-3 Gibson+10 HAT-P-3 Adams+10 OGLE-TR-113 Bean 09 CoRoT-exo-1 Csizmadia+10 CoRoT-exo-1
The Frustration GJ 1214 Carter et al. 2010
Architectures of Other Planetary Systems Basic facts: • Planet number • Masses • Radii Dynamical properties: • Periods (n.b.: their ratios) • Eccentricities • Mutual Inclinations w/ TTV w/ TTV w/ TTV w/ TDV Science Goals: Mass-Radius measurements (Composition) Planet Discovery / Full Architectures Resonant dynamics Migration Constraints
Results from Kepler • Unique masses: Kepler-9, 11, 18, 30, 36, KOI-1574 (Ofir et al.), KOI-152 (Jontof-Hutter et al.), KOI-620 (Masuda),KOI-314 (Kipping et al.) • Anti-correlation to confirm planethood(Ford et al. 2012, Steffen et al. 2013, Fabrycky et al. 2012, Ji-Wei Xie et al. arxiv:1308.3751, 1309.2329) • Anti-correlation to measure mass and eccentricity distributions(Lithwick et al. 2013, Hadden & Lithwick 2013, Xie 2014). • Clearinghouse of TTV and TDV curves (Mazehet al. 2013)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)
Kepler 9 MCMC of TTV published (w/ RVs) Mb=42.3±0.6 ME* 80±4 ME Mc= 29.1±0.6 ME* 54±8 ME *(1.0 Mhost assumed) • 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010) • See also Ofir & Dreizler
Fits to all TTVs • Chose the large-amplitude, distinctive TTV shapes. • Found dynamical fits to them, and explored uncertainties by DEMCMC • Extrapolated that cloud of fits to future times, for follow-up observations • Needed to invoke additional planets in some multi-transiting systems.
Kepler-30 Fabrycky, Ford, Steffen et al. 2012
Systems with Distinctive O-C • KOI-872 (Nesvorny et al. 2012) P/P = 1.696
Systems with Distinctive O-C • KOI-872 (Nesvorny et al. 2012) P/P = 1.696
KOI-872 (Nesvorny et al. 2012) P/P = 1.697 P/P = 2.43 Kepler-19 Ballard, Fabrycky, et al. 2011 Inversion including inclination: Nesvorny et al. (2008,09,10)
Spitzer TTV program Spitzer program. • Spitzer program p10127 • Not hot Jupiters • Deep transits • Long-period = Long durations
KOI-1426 d c b Unique solutions KOI-872 (Nesvorny+12) KOI-1474 (Dawson+12) KOI-142(Nesvorny+13)
KOI-351 = Kepler 90 Kepler-90h; P=330 days
Planes: 13,600km Neutrinos: 11,100km Time zones: 12 http://www.gcmap.com/
KOINet:Carolina van Essen (Gottingen / Stefan Dreizler) Other efforts: Ciardi (KFOP) Pepper (colleges) Santerne Gary (amateur) # targets: A few dozen. Depends strongly on precision. http://www.gcmap.com/
Summary • Kepler is a machine for finding multiplanet systems, both multi-transiting and perturbed systems • TTVs are unveiling full system architectures and additional planets, even in multi-transiting systems. • Following these transit times, world-wide, will be a major effort and legacy of Kepler.