Modeling and Observing Kepler Planetary Systems with Large TTVs Daniel Fabrycky*, Eric Agol, Kevin Stevenson, Sarah Ballard, Roberto Sanchis-Ojeda, Joshua Winn, Matthew Holman, Tsevi Mazeh, Kepler Team and the World *Sloan Fellowship *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 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

1471 planets in 588 systems.

Architectures of Other Planetary Systems Transits Radial Velocities ✔ ✔✔ 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 (Mazeh et 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 Mb= 42.3±0.6 ME* 80±4 ME Mc= 29.1±0.6 ME* 54±8 ME 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 M host 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.

MCMC chains

Differential Evolution MCMC

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

Inversion including inclination: Nesvorny et al. (2008,09,10) KOI-872 (Nesvorny et al. 2012) Kepler-19 Ballard, Fabrycky, et al. 2011 P/P = 1.697 P/P = 2.43 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 Unique solutions KOI-872 (Nesvorny+12) KOI-1474 (Dawson+12) c b Unique solutions KOI-872 (Nesvorny+12) KOI-1474 (Dawson+12) KOI-142 (Nesvorny+13)

Cabrera et al. 2013, Agol et al. in prep

KOI-351 = Kepler 90 Kepler-90h; P=330 days Made by Fabrycky (PI P10127) Takes ~80 seconds, if well-rehearsed. “Exoplanets. Planetary System Architecture by Transit Timing.” Start playing movie and read the upper bullet points. Click for transit timing diagram. Say: “This is the timing variations of the outer two planets of this system. The blue constraints are inferred from the Kepler data. The red data will be taken by Spitzer, resulting in the red constraints going forward. The system will then be “solved,” with planetary masses precise to a few percent.” Click for the transit curve. “The first transit has already been obtained and came roughly when expected, indicating no more big 8th planets exterior to it. The next two are scheduled.” Click for science goals. “This example adds two points to the mass-radius diagram for cool giant planets, and it teaches us the orbits and constraints on additional planets for the richest exoplanet system. Other systems will teach us about migration through resonances among planets.”

Planes: 13,600km Neutrinos: 11,100km Time zones: 12 http://www.gcmap.com/

Other efforts: Ciardi (KFOP) Pepper (colleges) Santerne Gary (amateur) 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.