New Results from Kepler: Systems of Multiple Transiting Planets

w/ Correlated TTVs

Eric B. FordExtreme Solar Systems II

September 12, 2011

Based on a series of papers recently or soon to be submitted withmajor 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-gKepler-10 b&c

Confirmed Multiple Transiting Planet Systems

115 doubles, 45 triples, 8 quads, 1 of five & 1 of six!Borucki et al. 2011bLissauer 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 168.03

KOI 168.01

Ford et al. submitted to ApJ

Folded Light Curves Observed Transit Times

KOI 168.03

KOI 168.01

Folded Light Curves Observed Transit Times

Num

ber

of D

ata

Set

s

KOI 168.03KOI 168.03KOI 168.03

KOI 168.01

KOI 168.03

KOI 168.01

KOI 168.03

KOI 168.01

KOI 168.03

KOI 168.01

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

Ξmax

Ford et al. submitted to ApJ Steffen et al. in prep.

PermutedData Sets

PermutedData Sets

ActualData Set

ActualData Set

Correlation Coefficient Between Smoothed TTV Curves

Maximum Power at Common Fourier Frequency

Num

ber

of D

ata

Set

s

Significance of TTVs in KOI 168

Fabrycky et al. in prep.

PermutedData Sets

PermutedData Sets

ActualData SetActual

Data Set

Amplitude of Sinusoidal Fit at Predicted TTV Period

KOI 168.01 KOI 168.03

Calculate false alarm probability <<10-3 via Monte Carlo with permuted data sets

Stability Implies Planetary Masses

Ford et al. submitted to ApJ

Inst

abili

ty T

ime

(yr)

Planet Mass (MJup)

Max

imum

Mas

s

Max

imum

Mas

s

N-Body integrations includeonly two confirmed planetsAssume 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 168.03 168.01 168.02

Period (d) 7.11 10.7 15.3

Duration (hr) 4.8 6.1 5.7

Rp (RE) 1.9 3.2 2.2

Maximum Mp (MJ) (Stability) 0.8 2.7 NA

Best-Fit Mp (ME) (Circular) 12 ± 2 22 ± 6 NA

Best-Fit Mp (ME) (Eccentric) 5 ± 16 15 ± 50 NA

Best-Fit e 0.07 ± 0.6 0.07 ± 0.5 NA

Best-Fit χ2 (No TTVs) 140 81 6

Best-Fit χ2 (Circular) 124 48 6

Best-Fit χ2 (Eccentric) 112 38 6

Number of Transit Times 65 44 32

Stellar Parameters

KOI 168 KIC Spectra

Kp 13.4

Teff (K) 5877 5760 ±124

Log g 4.0 4.0 ±0.14

[M/H] -0.33 -0.09 ±0.14

M* (Msol) 1.21 1.1 ± 0.1

R* (Rsol) 1.88 1.5 ± 0.3

L* (Lsol) 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 SpaceTTVs can confirm planets around:• Faint stars

Median 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

RVBlenderTTVs

TTVs Expand Kepler’s Search SpaceTTVs can confirm planets around:• Faint stars

Median 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

(upcoming papers)

RVBlenderTTVs

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

Future Prospects KOI 500

Questions

NASA

Example of Correlated TTVs

KOI 168.03

KOI 168.01

Ford et al. submitted to ApJ

TTVs in Nominal, Circular Model Observed Transit Times

KOI 168.03

KOI 168.01

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

Ass

umpt

ions

abo

ut T

TV

Sig

nal

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 <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)

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. 2010

Kepler-9

Ford et al. submitted to ApJ