New Results from Kepler: Systems of Multiple Transiting Planets w/ Correlated TTVs Eric B. Ford Extreme Solar Systems II September 12, 2011 Based on a series of papers recently or soon to be submitted with major contributions from the Kepler TTV Working Group (especially Bryson, Carter, Cochran, Desert, Fabrycky, Ford, Fressin, Holman, Latham, Lissauer, Marcy, Moorhead, Morehead, Ragozzine, Rowe, Steffen, Welsch), the Kepler Follow-Up Observation Program & the entire Kepler Science Team

Kepler-9 b-d Kepler-11 b-g Kepler-10 b&c Confirmed Multiple Transiting Planet Systems

115 doubles, 45 triples, 8 quads, 1 of five & 1 of six! Borucki et al. 2011b Lissauer et al. 2011b Hundreds More Systems with Multiple Transiting Planet Candidates

Transit Timing Variations (TTVs) Confirmed & Characterized Kepler-9 b&c Holman et al. 2010

Opportunities & Challenges for TTVs Kepler detects dozens of TTV candidates (Ford+ 2011) Complex TTV signatures (e.g., Veras+ 2011) Multiple transiting planet systems easier to interpret & provide stronger constraints (Ragozzine & Holman 2011) Focus on these for prompt science results Shortest TTV timescale is often ~years Detailed modeling requires years of data → big benefit from extended mission!

A New Method to Confirm Multiple Transiting Planet Systems Demonstrate 2 objects are in the same system –Full physical model for TTVs Kepler-9 (Holman+ 2010): 1:2 MMR dominates Kepler-11 (Lissauer+ 2011): Non-resonant –Correlated TTVs for two KOIs (Ford+ 2011) –TTVs w/ common timescale (Steffen+ 2011) –TTVs at predicted timescale (Fabrycky+ 2011) Place limits on masses via orbital stability → Confirm Multiple Planet Systems

Example of Correlated TTVs KOI KOI Ford et al. submitted to ApJ Folded Light CurvesObserved Transit Times

KOI KOI Folded Light CurvesObserved Transit Times Number of Data Sets KOI KOI KOI KOI KOI KOI KOI KOI Example of Correlated TTVs Ford et al. submitted to ApJ

Significance of TTVs in KOI 168 Calculate false alarm probability <<10 -3 via Monte Carlo with permuted data sets Ξ max Ford et al. submitted to ApJSteffen et al. in prep. Permuted Data Sets Actual Data Set Correlation Coefficient Between Smoothed TTV Curves Maximum Power at Common Fourier Frequency

Number of Data Sets Significance of TTVs in KOI 168 Fabrycky et al. in prep. Permuted Data Sets Actual Data Set Amplitude of Sinusoidal Fit at Predicted TTV Period KOI KOI Calculate false alarm probability <<10-3 via Monte Carlo with permuted data sets

Stability Implies Planetary Masses Ford et al. submitted to ApJ Instability Time (yr) Planet Mass (M Jup ) Maximum Mass N-Body integrations include only two confirmed planets Assume coplanar, circular orbits & planet mass ratio based on planet radius ratio

Properties of KOI 168 System Inner two planets confirmed by TTVs + stability Large uncertainties in planet masses –Don’t put on a mass-radius diagram (yet)! –Continued observations needed to break degeneracy w/ eccentricity Period ratios near 4:6:9 Planetary Parameters Period (d) Duration (hr) R p (R E ) Maximum M p (M J ) (Stability)0.82.7NA Best-Fit M p (M E ) (Circular)12 ± 222 ± 6NA Best-Fit M p (M E ) (Eccentric) 5 ± 1615 ± 50NA Best-Fit e0.07 ± ± 0.5NA Best-Fit χ 2 (No TTVs)14081 ̶ Best-Fit χ 2 (Circular)12448 ̶ Best-Fit χ 2 (Eccentric)11238 ̶ Number of Transit Times Stellar Parameters KOI 168KICSpectra Kp13.4 Teff (K) ±124 Log g ±0.14 [M/H] ±0.14 M * (M sol ) ± 0.1 R * (R sol ) ± 0.3 L * (L sol )2.3 Age (Gyr)4 - 8 Ford et al. submitted to ApJ

TTVs Poised to Confirm Twelve More Systems with Multiple Transiting Planets 24 more planets would be confirmed (5 papers in the works) Period ratios of these pairs: –Five within 4% of 2:1 MMR –Five within 2% of 3:2 MMR –Two even closer (Period ratios ~1.3 and ~1.4)! 12 additional transiting planet candidates in these same systems At least 1 planet confirmable independently (RVs, Spitzer, Blender) in 4 systems

TTVs Expand Kepler’s Search Space TTVs can confirm planets around: Faint stars Median Kp = 15.2 Stars w/o RVs With extended time baseline TTVs offer: Precise masses for short-period planets Confirmation of closely spaced systems in HZ RV Blender TTVs

TTVs Expand Kepler’s Search Space TTVs can confirm planets around: Faint stars Median Kp = 15.2 Stars w/o RVs With extended time baseline TTVs offer: Precise masses for short-period planets Confirmation of closely spaced systems in HZ (upcoming papers) RV Blender TTVs

Observations (short-term) Nominal Model (long-term) TTV timescales often ~ years Sensitivity of TTVs is increasing as ~t 5/2 Expect to confirm & characterize many more planets via TTVs Strengthens case for an extended mission Ford et al Future Prospects KOI 500

Questions NASA

Example of Correlated TTVs KOI KOI Ford et al. submitted to ApJ TTVs in Nominal, Circular ModelObserved Transit Times KOI KOI

Mass & Eccentricity Limits for KOI 168

Three Tests for Significance of TTVs in Systems with Multiple Transiting Planets Method 1 (Ford et al.): Interacting planets have anticorrelated TTVs. Assume nothing about their form, but apply generalized statistical methods (Gaussian Process) to construct a time series for two objects. Show that those two time series are anticorrelated. Method 2 (Steffen et al.): Interacting planets have anticorrelated TTVs. Assume TTVs are nearly sinusoidal with same timescale. Show that both TTV signals have power at common timescale. Method 3 (Fabrycky et al.): Observed orbital periods predict TTV timescale. Test for sinusoidal TTV signal at a single predicted frequency. All three methods measure the significance of TTV signal via Monte Carlo simulations, permuted TTVs.

NA 935: Basis of TTV Detections 168: 244: 738: 806: 841: 952: 1102: 870: 250: Ford et al. Gaussian Process NA Steffen et al. Fourier Fabrycky et al. TTV Timescale NA

Sensitivity to Most Common TTV Signals Assumptions about TTV Signal Increasing Generality Ford Steffen Fabrycky

Additional Tests & Analysis Key tests for confirmation by TTVs (all) –KOI host has multiple transiting planet candidates –At least two neighboring candidates have anticorrelated TTVs –Orbital stability dictates a maximum mass in planetary regime Additional Tests Passed (exceptions in paren) –Centroid offset during transit <3 σ (w/ multi-Q DV); i.e., consistent with KOIs around target star (841 now resolved) –Odd-Even Depth statistic <3 σ; i.e., no warning signs of EB (see discussion of exceptions: KOIs ) –Nominal orbital model is Dynamically stable Consistent with timescale of TTVs Additional FOP Observations –Imaging: Classical (all), Speckle (168, 244, 250, 870), AO (244) –Spectra: all hosts except 1102 ► Updated stellar parameters –Spitzer: depths in optical/IR are consistent (244, 250) –Doppler: 244 (but RVs complicated & saved for follow-up paper)

Causes of Transit Timing Variations Long term trends –Exchange of orbital energy (if near resonance) –Precession of orbits (if eccentric) –Light travel time (if massive/eccentric distant companion) Short-term variations (if closely spaced) Noise –Stellar activity –Measurement Holman et al Kepler-9

Ford et al. submitted to ApJ

Ford et al. submitted to ApJ