R. Dawson, SCMA, 06/09/16 Characterizing Kepler’s ...cschafer/SCMA6/Dawson.pdf · R. Dawson, SCMA, 06/09/16 Characterizing Kepler’s Transiting Planets in the Presence of Correlated

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]

1

10

Rp

[R⊕]

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

Five: 18 Six: 2 Seven: 1 1 RMars

1 RNeptune

1 RJupiter

Plan

et R

adiu

s (E

arth

)

1

10

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]

1

10

Rp

[R⊕]

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

Five: 18 Six: 2 Seven: 1 1 RMars

1 RNeptune

1 RJupiter

Plan

et R

adiu

s (E

arth

)

1

10

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⊕)

0

5

10

15

Rp (

R⊕)

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

Radi

us (E

arth

)

Mass (Earth)

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

http://exoplanets.eu


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]

0.94

0.96

0.98

1.00

no

rma

lize

d d

etr

en

de

d f

lux

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?

RID

et a

l. 20

12


Photometry

Planet detection



timeTT

VRevise formation

theories



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

time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014


500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014

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


500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014



500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014



500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014



500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014



500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

500 1000 1500time (days)

-2

-1

0

1

2

3

4

(O-C

) hours

0 30 90 115 145 165 Omegac (deg)

500 1000 1500time (days)

-2

-1

0

1

2

3

(O-C

) hours

500 1000 1500time (days)

-5

0

5

Resi

duals

(si

gm

a)

RID et al. 2014



−5 0 5(time − C [BJD−2455000]) [hrs]

0.94

0.96

0.98

1.00

norm

aliz

ed d

etr

ended flu

x

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

RID

et a

l. 20

12


We know the Kepler-419 dataset contains correlated noise

5 10 15lag (days)

−0.2

−0.1

0.0

0.1

0.2

DC

F

flux

powe

r

RID et al. 2012


Common behavior: three segment spectrum

powe

r

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]

0.94

0.96

0.98

1.00

no

rma

lize

d d

etr

en

de

d f

lux

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?

RID

et a

l. 20

12



powe

r

f-2

Chunk

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

(O-C

) hou

rs

500 1000 1500time (days)

-4

-2

0

2

delta

tim

e (m

in)

500 1000 1500time (days)

0.4

0.3

0.2

0.1

0.0

impa

ct p

aram

eter

, b

6 7 8 9 10 11 ρ circ

0.00.20.40.60.81.0

Rela

tive

prob

abilit

y

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

02468

fath

er c

oeffi

cien

t

0 200 400 600 800 1000translation

-3-2-10123

norm

aliz

ed fl

ux

0.001 0.010 0.100frequency (c/d)

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

pow

er

Wavelet transform computes power

for different translations and

scales

scal

e256 64 16 4 1

White noise


Wavelet transform computes power

for different translations and

scales

scal

e

0 200 400 600 800 1000translation

02468

fath

er c

oeffi

cien

t

0 200 400 600 800 1000translation

-10123

norm

aliz

ed fl

ux

0.001 0.010 0.100frequency (c/d)

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

pow

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

trans

latio

n


Gaussian process generated with Matern kernel in frequency space

0 5 10 15 20time (days)

0.9990

0.9995

1.0000

1.0005

flux

0.1 1.0 10.0frequency (c/d)

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

pow

er

f-2 white component



powe

r

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

flux

0.1 1.0 10.0frequency (c/d)

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

pow

er

f-2 white component



powe

r

f-2

Chunk

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)

10-4

10-2

100

102

104

red

nois

e (p

pm) no polynomial



simultaneous line

10-4 10-2 100 102 104

white noise (ppm)

10-4

10-2

100

102

104

red

nois

e (p

pm)



simultaneous polynomial

10-4 10-2 100 102 104

white noise (ppm)

10-4

10-2

100

102

104

red

nois

e (p

pm)


simultaneous line

Kepler sun-like star properties: GPR likelihood

10-4 10-2 100 102 104

white noise (ppm)

10-4

10-2

100

102

104

red

nois

e (p

pm)


simultaneous polynomial


10-4 10-2 100 102 104

white noise (ppm)

10-4

10-2

100

102

104

red

nois

e (p

pm)



no polynomial

10-4 10-2 100 102 104

white noise (ppm)

10-4

10-2

100

102

104

red

nois

e (p

pm)


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

PDF

-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

-2

0

2

4

6

Incr

ease

in d

evia

tion

(min

utes

)

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)

RV

0 500 1000 1500

-1.0

-0.5

0.0

0.5

1.0Am

plitu

de

0.1 1.0 10.0 100.002

4

6

8

10

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


velo

city

frequency (day-1)

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

Aliasing and activity cycles


Robertson+ 14

Less time sampling during inactive cycle

Gl 581


velo

city

frequency (day-1)

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700-2

-1

0

1

2

0.005 0.010 0.015 0.020 0.0250.00.2

0.4

0.6

0.8

1.0

1.2

Aliasing and activity cycles


0.008 0.010 0.012 0.014 0.016 0.018 0.0200

500

1000

1500

0.008 0.010 0.012 0.014 0.016 0.018 0.0200

500

1000

1500

frequency (day-1)

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

prob

abilit

y of

reco

very

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

500

1000

1500

0.008 0.010 0.012 0.014 0.016 0.018 0.0200

500

1000

1500

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!

Documents

R. Dawson, SCMA, 06/09/16 Characterizing Kepler’s ...cschafer/SCMA6/Dawson.pdf · R. Dawson, SCMA, 06/09/16 Characterizing Kepler’s Transiting Planets in the Presence of Correlated