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
R. Dawson, SCMA, 06/09/16
Kepler space telescope monitored the brightness of hundreds of thousands of stars
R. Dawson, SCMA, 06/09/16
Star dims during planetary transit
Earth-sized: 80 ppmImage Credit: NASA
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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?
R. Dawson, SCMA, 06/09/16
Image Credit: NASA Ames Research Center/Kepler Mission
Gravitational interactions between planets cause transit timing variations
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Photometry
Planet detection
Transit time inference
dynamical models of transit times
timeTT
VRevise formation
theories
Population inference
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Photometry
Planet detection
Transit time inference
dynamical models of transit times
timeTT
VRevise formation
theories
Population inference
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
−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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Common behavior: three segment spectrum
powe
r
f-2 white component
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Common behavior: three segment spectrum
powe
r
f-2
Chunk
white component
R. Dawson, SCMA, 06/09/16
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)
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Gaussian process regression likelihood:
prescription for covariance matrix
implemented using dan.iel.fm/george
Radial Matern 5/2 kernel
translation
trans
latio
n
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Common behavior: three segment spectrum
powe
r
f-2 white component
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Common behavior: three segment spectrum
powe
r
f-2
Chunk
white component
R. Dawson, SCMA, 06/09/16
Noise properties of Sun-like Kepler stars
R. Dawson, SCMA, 06/09/16
Sometimes white-noise dominatese.g., sun-like star
KIC 12011630
σw=35±1 ppm
R. Dawson, SCMA, 06/09/16
Simultaneous linear fitting: sometimes sufficient
e.g., sun-like star KIC 8374139σw=106±8 ppm, σr=700±40 ppm σw=150±5 ppm
R. Dawson, SCMA, 06/09/16
Simultaneous polynomial fitting: sometimes sufficient
e.g., sun-like star KIC 3970397σw=88±2 ppm, σr=53±5 ppm σw=86±3 ppm
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Kepler sun-like star properties: wavelet likelihood
simultaneous line
10-4 10-2 100 102 104
white noise (ppm)
10-4
10-2
100
102
104
red
nois
e (p
pm)
R. Dawson, SCMA, 06/09/16
Kepler sun-like star properties: wavelet likelihood
simultaneous polynomial
10-4 10-2 100 102 104
white noise (ppm)
10-4
10-2
100
102
104
red
nois
e (p
pm)
R. Dawson, SCMA, 06/09/16
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)
R. Dawson, SCMA, 06/09/16
simultaneous polynomial
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)
R. Dawson, SCMA, 06/09/16
Kepler sun-like star properties: GPR likelihood
no polynomial
10-4 10-2 100 102 104
white noise (ppm)
10-4
10-2
100
102
104
red
nois
e (p
pm)
R. Dawson, SCMA, 06/09/16
Kepler sun-like star properties: Gaussian process regression, timescale
log10 tau
no line line polynomial
R. Dawson, SCMA, 06/09/16
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)
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Photometry
Planet detection
Transit time inference
dynamical models of transit times
timeTT
VRevise formation
theories
Population inference
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Extra slides
R. Dawson, SCMA, 06/09/16
The radial-velocity technique
Image Credit: ESO/L. CalçadaEarth twin: 10 cm/s
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Time sampling complicates RV interpretation
55 Cnc e GJ 581d Alpha Cen b
One of first mini-Neptunes
discoveredOrbits nearby
starHabitable zone
super-Earth
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Use the fingerprint of multiple aliasesRID & Fabrycky 2010
55 Cnc
frequency (day-1)
Window function
Fischer+08 dataset
RID & Fabrycky 2010
f = | f ± f | alias true sample
R. Dawson, SCMA, 06/09/16
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
f = | f ± f | alias true sample
R. Dawson, SCMA, 06/09/16
Time sampling complicates RV interpretation
55 Cnc e GJ 581d Alpha Cen b
One of first mini-Neptunes
discoveredOrbits nearby
starHabitable zone
super-Earth
R. Dawson, SCMA, 06/09/16
Gl 581 d: alias ambiguityUdry: 07: P = 84 days
Mayor+ 09: P = 67 days
RID & Fabrycky 10: P = ?
Robertson+ 14: Stellar activity
R. Dawson, SCMA, 06/09/16
Stellar activity: a stochastic, quasi-periodic signal
Mathur+ 14
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Robertson+ 14
Less time sampling during inactive cycle
Gl 581
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
Time sampling complicates RV interpretation
55 Cnc e GJ 581d Alpha Cen b
One of first mini-Neptunes
discoveredOrbits nearby
starHabitable zone
super-Earth
R. Dawson, SCMA, 06/09/16
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
R. Dawson, SCMA, 06/09/16
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!