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

*U Chicago *Sloan Fellowship

Transit Timing Variations

Agol et al. 2005, Murray & Holman 2005

The Promise

Agol, Steffen, Sari, Clarkson (2005)

The Frustration

HD 209458

TrES-2

Steffen & Agol 2005

Agol & Steffen 2007

The Frustration

Miller-Ricci+07

HD209458

Miller-Ricci+07

HD189733Miller-Ricci+06HD189733 Ballard+10

GJ436

Gibson+10

HAT-P-3

Gibson+10

TrES-3

Adams+10

OGLE-TR-113

Adams+10

OGLE-TR-113

Bean 09

CoRoT-exo-1 Csizmadia+10

CoRoT-exo-1

The FrustrationGJ 1214 Carter et al. 2010

Architectures of Other Planetary Systems

Basic facts:• Planet number• Masses• RadiiDynamical properties:• Periods (n.b.: their ratios)• Eccentricities• Mutual Inclinations

Transits Radial Velocities✔

✔

✔

✔✔ ✔

✔w/ TDV

w/ TTV

w/ TTV

w/ TTV

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

• 2 gas giants, TTV’ing (Holman, Fabrycky, et al. 2010)

• See also Ofir & Dreizler

Mb

= 42.3±0.6 ME

* 80±4 ME

Mc= 29.1±0.6 M

E* 54±8 M

E

*(1.0 M

host assumed)

MCMC of TTV published (w/ RVs)

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

• 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

b

c

d

Unique solutions

KOI-872 (Nesvorny+12)

KOI-1474 (Dawson+12)

KOI-142 (Nesvorny+13)

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

Kepler-90h; P=330 days

KOI-351 = Kepler 90

Planes:13,600km

Neutrinos:11,100km

Time zones:12

http://www.gcmap.com/

• KOINet:Carolina van Essen (Gottingen / Stefan Dreizler)

http://www.gcmap.com/

Other efforts:

Ciardi (KFOP)

Pepper (colleges)

Santerne

Gary (amateur)

# targets:

A few dozen.

Depends strongly on

precision.

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.