R. Dawson, SCMA, 06/09/16 Characterizing Kepler’s ...cschafer/SCMA6/Dawson.pdf · R. Dawson,...

R. Dawson, SCMA, 06/09/16

Characterizing Kepler’s Transiting Planets in the Presence of Correlated Noise

Rebekah (Bekki) Dawson Penn State, Center for Exoplanets and Habitable Worlds

Acknowledgments: SAMSI Noise and Detrending Working Group (incl. Daniel Foreman-Mackey, Eric Ford, Ben Montet, Tom Loredo, Ruth Angus, Billy Quarles, Ian Czekala, Robert Wolpert, Jogesh Babu, Tom Barclay, David Hogg); Patricio Cubillos, Josh Carter

Kepler space telescope monitored the brightness of hundreds of thousands of stars

Star dims during planetary transit

Earth-sized: 80 ppmImage Credit: NASA

Kepler discovered thousands of close-in planets

1 10 100Orbital Period [days]

[R⊕]

One: 2117 Two: 384 Three: 134 Four: 48

Five: 18 Six: 2 Seven: 1 1 RMars

1 RNeptune

1 RJupiter

Orbital Period (days)100101

Lissauer, RID, & Tremaine 2014,Nature review

Kepler candidate discoveries: Borucki+11ab, Batalha+ 12, Burke+ 14, Mullaly+15

Kepler discovered thousands of planets

1 10 100Orbital Period [days]

[R⊕]

One: 2117 Two: 384 Three: 134 Four: 48

Five: 18 Six: 2 Seven: 1 1 RMars

1 RNeptune

1 RJupiter

Orbital Period (days)100101

Lissauer, RID, & Tremaine 2014,Nature review

Kepler candidate discoveries: Borucki+11ab, Batalha+ 12, Burke+ 14, Mullaly+15

Outstanding question: where did these planets come from?

Image Credit: NASA Ames Research Center/Kepler Mission

Gravitational interactions between planets cause transit timing variations

Transit timing variations essential to understanding where close-in planets come from

Resonant orbits [with low libration amplitudes]Ultra-puffiese.g.,

Kepler-223, Mills et al. 2016 Nature

1 10 100 1000Mp (M⊕)

10-200 day orbital periods; taken from exoplanets.eu; non-circumbinary

Mass (Earth)

e.g. Jontof-Hutter et al. 2014, formation: Lee & Chiang 2016

Photometry

Planet detection

Transit time inference

dynamical models of transit times

timeTT

VRevise formation

theories

Population inference

Kepler data key characteristics

Time span: 4 years Cadence: 30 minutes (1 minute), evenly spaced Noise floor: 15 ppm

Earth-like transit signal: 80 ppm, 12 hour duration, 1 year period

Case study: how did Kepler-419b achieve its close-in, highly elliptical orbit?

−5 0 5(time − C [BJD−2455000]) [hrs]

C = −40.665KOI−1474

C = 29.068

C = 98.802

C = 168.536

C = 238.271

C = 308.005

C = 377.739

C = 447.473

Is its non-transiting companion orbiting in the same plane?

Photometry

Planet detection

timeTT

VRevise formation

theories

The companion’s inclination has a subtle effect on the signal500 1000 1500

time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

The companion’s inclination has a subtle effect on the signal

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

) hours

500 1000 1500time (days)

RID et al. 2014

−5 0 5(time − C [BJD−2455000]) [hrs]

ended flu

C = −40.665KOI−1474

C = 29.068

C = 98.802

C = 168.536

C = 238.271

C = 308.005

C = 377.739

C = 447.473

We know the Kepler-419 dataset contains correlated noise

5 10 15lag (days)

−0.2

−0.1

RID et al. 2012

Common behavior: three segment spectrum

f-2 white component

Case study: how did Kepler-419b achieve its close-in, highly elliptical orbit?

−5 0 5(time − C [BJD−2455000]) [hrs]

C = −40.665KOI−1474

C = 29.068

C = 98.802

C = 168.536

C = 238.271

C = 308.005

C = 377.739

C = 447.473

Is its non-transiting companion orbiting in the same plane?

white component

Pre-detrending the data can lead to errors in the inferred planet properties

Barclay et al. 15, Kepler-91b Gaussian process regression correlated noise using george (Foreman-Mackey et al. in prep)

Previous pre-whitening treatment caused this planet to be

misdiagnosed as an astrophysical false positive (Sliski & Kipping 14)

Two different correlated noise treatments yield consistent transit times

500 1000 1500time (days)

-2-10123

500 1000 1500time (days)

6 7 8 9 10 11 ρ circ

0.00.20.40.60.81.0

abilit

Median filter detrending, Carter & Winn 2009 wavelet likelihood Foreman-Mackey et al. in prep. Gaussian process regression likelihood with squared exponential covariance kernel, dan.iel.fm/george

RID et al. 2014

0 200 400 600 800 1000translation

-3-2-10123

0.001 0.010 0.100frequency (c/d)

10-610-510-410-310-210-1

Wavelet transform computes power

for different translations and

scales

e256 64 16 4 1

White noise

Wavelet transform computes power

for different translations and

scales

0 200 400 600 800 1000translation

-10123

0.001 0.010 0.100frequency (c/d)

10-610-510-410-310-210-1

er256 64 16 4 1

Pink (1/f) noise

Wavelet likelihood method parametrizes noise into red σr and white σw component

Carter & Winn 2009 (144 citations) based on Wornell 1996:

Signal Processing with Fractals: A Wavelet-Based Approach

Dictated relationship between scale coefficients for 1/fᵞ noise

Gaussian process regression likelihood:

prescription for covariance matrix

implemented using dan.iel.fm/george

Radial Matern 5/2 kernel

translation

Gaussian process generated with Matern kernel in frequency space

0 5 10 15 20time (days)

0.9990

0.9995

1.0000

1.0005

0.1 1.0 10.0frequency (c/d)

10-1410-1310-1210-1110-1010-910-8

f-2 white component

Gaussian process generated with Matern kernel in frequency space

0 5 10 15 20time (days)

0.9990

0.9995

1.0000

1.0005

0.1 1.0 10.0frequency (c/d)

10-1410-1310-1210-1110-1010-910-8

f-2 white component

white component

Noise properties of Sun-like Kepler stars

Sometimes white-noise dominatese.g., sun-like star

KIC 12011630

σw=35±1 ppm

Simultaneous linear fitting: sometimes sufficient

e.g., sun-like star KIC 8374139σw=106±8 ppm, σr=700±40 ppm σw=150±5 ppm

Simultaneous polynomial fitting: sometimes sufficient

e.g., sun-like star KIC 3970397σw=88±2 ppm, σr=53±5 ppm σw=86±3 ppm

Simultaneous polynomial fitting: sometimes insufficient

e.g., sun-like star KIC 4819602σw=0±10 ppm, σr=8799±200 ppm σw=64±8 ppm, σr=580±30 ppm

Kepler sun-like star properties: wavelet likelihood

10-4 10-2 100 102 104

white noise (ppm)

pm) no polynomial

simultaneous line

10-4 10-2 100 102 104

white noise (ppm)

simultaneous polynomial

10-4 10-2 100 102 104

white noise (ppm)

simultaneous line

Kepler sun-like star properties: GPR likelihood

10-4 10-2 100 102 104

white noise (ppm)

simultaneous polynomial

10-4 10-2 100 102 104

white noise (ppm)

no polynomial

10-4 10-2 100 102 104

white noise (ppm)

Kepler sun-like star properties: Gaussian process regression, timescale

log10 tau

no line line polynomial

Correlated noise treatment: key questions

• Which stars merit a correlated noise treatment?

• How do we optimize the use of out-of-transit data to infer noise hyperparameters?

• Do wavelet likelihood functions or Gaussian process regression likelihood functions perform better? Which wavelet families and noise power law (wavelets) or kernels (GP regression) is best suited?

• What degree polynomial, if any, should be simultaneously fit to each data chunk?

• How do correlated noise treatments perform on short cadence data? (1 min vs. 30 min cadence)

Example transit time posteriors Better recovery when accounting for correlated noise

(red dashed) and multi-modal posteriors captured

-20 -10 0 10 20-20 -10 0 10 20 -20 -10 0 10 20 -20 -10 0 10 20

WhiteGP

-20 -10 0 10 20

-50 0 50

-50 0 50 -50 0 50 -50 0 50

-40 -20 0 20 40 -40 -20 0 20 40 -40 -20 0 20 40 -40 -20 0 20 40Recovered - injected transit time (minutes) RID

Model 1: Joint modeling of transits + line with white noise likelihood Model 2: Joint modeling of transits + line with Gaussian process likelihood

Worse recovery when correlated noise is not accounted for in the likelihood

0 20 40 60 80 100Percentile

Based on fits to 50 sets of 16 injected transits for Sun-like star with significant correlated noise

R. Dawson, IAU

Summary and future work• Systematic study of correlated noise treatment for

inferring transit times is underway; will only be relevant for subset of stars

• Correlated noise treatment needs to be assessed for its impact on other key transit observables, e.g., depth, duration

• Correlated noise is an even more severe problem for radial velocity method of planet detection and characterization, including interplay of noise and aliasing due to gaps in time sampling

Photometry

Planet detection

timeTT

VRevise formation

theories

Summary and future work• Systematic study of correlated noise treatment for

inferring transit times is underway; will only be relevant for subset of stars

• Correlated noise treatment needs to be assessed for its impact on other key transit observables, e.g., depth, duration

• Correlated noise is an even more severe problem for radial velocity method of planet detection and characterization, including interplay of noise and aliasing due to gaps in time sampling

Extra slides

The radial-velocity technique

Image Credit: ESO/L. CalçadaEarth twin: 10 cm/s

Transit vs. radial-velocity

challengesTransit

(mostly space)Radial-velocity

(ground)

Time sampling Even, continuous Uneven, gaps

Planet duty cycle

A priori planet probability

Low (0.3% for Earth twin) 100% (but 0% for other line diagnostics)

High (≥~50%)Low (~few percent)

Datapoints ~100 ~100,000 or more

Signal repetition Detectable changes in period, duration

Undetectable for most planets

Time sampling complicates RV interpretation

55 Cnc e GJ 581d Alpha Cen b

One of first mini-Neptunes

discoveredOrbits nearby

starHabitable zone

super-Earth

Radial velocity sampling cadence -> aliases

time (days)

0 500 1000 1500

0.1 1.0 10.0 100.002

f = | f ± f | alias true sample

frequency (cycles/day)

Noise-free sinusoid with

Gl 581 HARPS sampling

Use the fingerprint of multiple aliasesRID & Fabrycky 2010

55 Cnc

frequency (day-1)

Window function

Fischer+08 dataset

RID & Fabrycky 2010

A revised, ultra-short period for 55 Cnc e

RID & Fabrycky 2010frequency (day-1)

55 Cnc e

0.74 day

Fischer+08 dataset

2.8 day

starHabitable zone

super-Earth

Gl 581 d: alias ambiguityUdry: 07: P = 84 days

Mayor+ 09: P = 67 days

RID & Fabrycky 10: P = ?

Robertson+ 14: Stellar activity

Stellar activity: a stochastic, quasi-periodic signal

Mathur+ 14

frequency (day-1)

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

Aliasing and activity cycles

Robertson+ 14

Less time sampling during inactive cycle

Gl 581

frequency (day-1)

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

300 400 500 600 700-2

0.005 0.010 0.015 0.020 0.0250.00.2

Aliasing and activity cycles

0.008 0.010 0.012 0.014 0.016 0.018 0.0200

frequency (day-1)

Stellar activity signal experiences extra aliasing when activity is low during sampling gap

abilit

activitysinusoid

Stellar activity signal experiences extra aliasing when activity is low during sampling gap

0.008 0.010 0.012 0.014 0.016 0.018 0.0200

frequency (day-1)

Aliasing ambiguities may tip us off about stellar activity

activitysinusoid

starHabitable zone

super-Earth

Alpha Cen b: the danger of pre-whitening

Dumusque+ 12: 1) detrend 2) fit planet parameters 3) check for aliasing

Rajpaul+15, 16 1) notice planet frequency in the window function 2) account for stellar activity simultaneous with

orbit fitting with Gaussian processes

Alpha Cen b: the danger of pre-whitening

Dumusque+ 12: 1) detrend 2) fit planet parameters 3) check for aliasing

Rajpaul+15, 16 1) notice planet frequency in the window function 2) account for stellar activity simultaneous with

orbit fitting with Gaussian processes f = | f ± f | alias true sample

long-term activity!

R. Dawson, SCMA, 06/09/16 Characterizing Kepler’s ...cschafer/SCMA6/Dawson.pdf · R. Dawson,...

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