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Based on a series of papers recently or soon to be submitted with

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

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Based on a series of papers recently or soon to be submitted with

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  1. New Results from Kepler: Systems of Multiple Transiting Planets w/ Correlated TTVs Eric B. FordExtreme Solar Systems IISeptember 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

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

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

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

  5. 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!

  6. 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

  7. KOI 168.03 KOI 168.01 Example of Correlated TTVs Folded Light Curves Observed Transit Times Ford et al. submitted to ApJ

  8. KOI 168.03 KOI 168.01 Example of Correlated TTVs Folded Light Curves Observed Transit Times KOI 168.03 KOI 168.03 KOI 168.03 KOI 168.03 KOI 168.03 KOI 168.03 Number of Data Sets KOI 168.01 KOI 168.01 KOI 168.01 KOI 168.01 Ford et al. submitted to ApJ

  9. Significance of TTVs in KOI 168 Calculate false alarm probability <<10-3via Monte Carlo with permuted data sets Correlation Coefficient Between Smoothed TTV Curves Maximum Power at Common Fourier Frequency PermutedData Sets ActualData Set ActualData Set PermutedData Sets Ξmax Ford et al. submitted to ApJ Steffen et al. in prep.

  10. Significance of TTVs in KOI 168 Calculate false alarm probability <<10-3 via Monte Carlo with permuted data sets Amplitude of Sinusoidal Fit at Predicted TTV Period KOI 168.01 KOI 168.03 Number of Data Sets ActualData Set ActualData Set PermutedData Sets PermutedData Sets Fabrycky et al. in prep.

  11. StabilityImpliesPlanetary Masses N-Body integrations includeonly two confirmed planets Assume coplanar, circular orbits & planet mass ratio based on planet radius ratio Instability Time (yr) Maximum Mass Maximum Mass Planet Mass (MJup) Ford et al. submitted to ApJ

  12. 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 Stellar Parameters Ford et al. submitted to ApJ

  13. 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

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

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

  16. Future Prospects KOI 500 Observations (short-term) Nominal Model(long-term) • TTV timescales often ~ years • Sensitivity of TTVs is increasing as ~t5/2 • Expect to confirm & characterize many more planets via TTVs • Strengthens case for an extended mission Ford et al. 2011

  17. Questions NASA

  18. Example of Correlated TTVs TTVs in Nominal, Circular Model Observed Transit Times KOI 168.03 KOI 168.03 KOI 168.01 KOI 168.01 Ford et al. submitted to ApJ

  19. Mass & Eccentricity Limits for KOI 168

  20. 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.

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

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

  23. 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 <3σ (w/ multi-Q DV); i.e., consistent with KOIs around target star (841 now resolved) • Odd-Even Depth statistic <3σ; i.e., no warning signs of EB (see discussion of exceptions: KOIs 806.03) • 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)

  24. Causes of Transit Timing Variations Kepler-9 • 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. 2010

  25. Ford et al. submitted to ApJ

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