The Architecture and Timing of Planetary Systems

Daniel Fabrycky Kevin Stevenson, Hannah Diamond-Lowe – University of Chicago Jack Lissauer, Darin Ragozzine, Jason Steffen,

Eric Agol, Sarah Ballard, and the Kepler team

Outline

•  Multi-transiting systems •  Mutual Inclination Measurements •  Systems with Large TTVs

Perryman 2013

Small planets are numerous

Mp sin i

Transits/Kepler (Howard et al. 2011)

Doppler/HARPS (Mayor et al. 2011) (Petigura, Howard, Marcy 2013)

Radial Velocity Multiple Planets

Kepler Mission (NASA,

2009-2013*) *resurrection as: K2

•  A search for Earth-like planets by the transit technique

•  Brightness measurements of 150,000 stars

•  In orbit around the Sun

Kepler-11

Lissauer, Fabrycky, Ford et al. 2011

10 20 30 40 50time [days] after September 25, 2009

0.9980

0.9985

0.9990

0.9995

1.0000

1.0005

flux

Courtesy J. Rowe., via Lissauer et al. 2014

Can we observe mutual inclinations in exoplanetary systems?

RV, not well. Kepler, yes. 1)  Statistics of Transiting Multiples (Lissauer, Ragozzine + 2011)

2)  Matching RV’s systems to Kepler’s (Tremaine & Dong 2011, Figueria + 2012)

3) Duration Ratio Statistics, explained next

Kepler-33 (Lissauer et al.)

Durations in Systems

Tdur

Durations in Systems

A variable to sense mutual inclinations:

> 1 [circular, coplanar] ~ 1 [uncorrelated]

Fabrycky, Lissauer, et al. 2014

Modeling mutual inclinations

Fabrycky, Lissauer, et al. 2014

Modeling mutual inclinations σi

Fabrycky, Lissauer, et al. 2014

Modeling mutual inclinations σi

Fabrycky, Lissauer, et al. 2014

Fitting Results

Fabrycky, Lissauer, et al. 2014

Planetary systems are flat

Solar System planets

Fabrycky, Lissauer, et al. 2014

Transit Timing Variations

Agol et al. 2005, Murray & Holman 2005

Dynamics: Orbital Timescales

Transit timing variations Agol et al. 2005, Murray & Holman 2005

Dynamics: Secular Timescales

P2/P1 = 2.44 near 5:2

Transit timing variations Agol et al. 2005, Murray & Holman 2005

Dynamics: Resonant Orbits

P2

/P1

= 2.00

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

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* Mc= 29.1±0.6 ME*

*(1.0 M¤ host assumed)

MCMC of TTV:

Embarrassment of Riches of TTV Kepler-9c Kepler-30b

Kepler-36c Kepler-30d

Kepler-9c Kepler-24c

Embarrassment of Riches of TTV

Kepler-29b

Kepler-23b

Kepler-24b

Nesvorny et al. 2012

Kepler-47b

Embarrassment of Riches of TTV

Kepler-25b Kepler-18b

Dawson et al. 2012

Kepler-11f

Architectures of Other Planetary Systems

Basic facts: •  Planet number •  Masses •  Radii Dynamical 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  (Composi8on)  Planet  Discovery  /  Full  Architectures  Resonant  dynamics  à  Migra8on  Constraints    

The Inverse Problem

In general, difficult degeneracies plague TTV inversions.

•  Perturbation theory (Agol et al. 2005 Appendix, Nesvorny & Morbidelli 2008, Nesvorny 2009, Nesvorny & Beauge 2009)

•  Numerical approach (Meschari et al. 2009, Meschari & Laughlin 2010)

•  Effects of Inclination near resonance (Payne et al. 2009) •  Extreme phase sensitivity (Veras et al. 2010)

5 minutes early

5 minutes late

Transit Times of Kepler-19b

Δχ2 of sinusoid, compared to linear = 250

Kepler-19 Ballard, Fabrycky, Fressin et al. 2011

O-C

(min

)

Lots of possible orbits for the planet Kepler-19c

Mean motion resonances: <2:3 >2:3 <2:1

Higher-order resonances: <1:3 <5:3 <3:1 >4:1

Co-orbital planet? Distant retrograde moon? 1:1

Possible orbits:

KOI-872 Nesvorny et al. 2012

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)

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.

Markov Chain Monte Carlo (MCMC) chains

Differential Evolution MCMC

Kepler-30

Fabrycky, Ford, Steffen et al. 2012

Spitzer TTV program

Spitzer program.

•  Spitzer program p10127 •  Not hot Jupiters •  Deep transits •  Long-period = Long durations •  Stevenson, Diamond-Lowe, Agol, Ballard

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

Kepler-­‐90h;  P=330  days  

KOI-­‐351  =  Kepler  90

KOI-1426

b c

d

Unique solutions KOI-872** (Nesvorny+12) KOI-1474 (Dawson+12) KOI-142 (Nesvorny+13) This one (Diamond-Lowe, Fabrycky et al., in prep)

A wild goose

Summary •  Kepler found a host of multiplanet systems. •  Statistics of multi-transiting systems à flat is typical. •  Full system architectures and additional planets are

revealed by transit timing.