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Data Challenges in Astronomy: NASA’s Kepler Mission and
the Search for Extrasolar Earths
Jon M. JenkinsSETI Institute/NASA Ames Research Center
Thursday September 22, 2011
STScISAO
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The Kepler Mission
What fraction of sun-like stars in our galaxy host potentially habitable Earth-size planets?
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How Hard is it to Find Good Planets?
Earth or Venus0.01% area of the Sun (1/10,000)
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Kepler Field Of View
Credit: Carter Roberts
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Kepler: Big Data, Big Challenges
Big Processing Challenges Instrument effects are large compared to signal of interest Observational noise is non-white and non-stationary ~100×106 tests per star for planetary signatures [O(N2)] Stellar variations are higher than expected
Big Data: >150,000 target stars 6x106 pixels collected and stored per ½ hour ~40 GB downlinked each month >40×109 points in the time series over 3.5 years
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The Kepler Science Pipeline: From Pixels To Planets
CALPixel Level
Calibrations
PAPhotometricAnalysis
Sums Pixels Together/Measures Star Locations
TPSTransiting
PlanetSearch
RawData
TCEs: Threshold Crossing Events
CorrectedLight Curves
CalibratedPixels
RawLight
Curves/Centroids
DVData
Validation
Diagnostic
Metrics
CALPixel Level
Calibrations
PAPhotometricAnalysis
Sums Pixels Together/Measures Star Locations
TPSTransiting
PlanetSearch
DVData
Validation
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Image Data
0.09x0.09 degrees80x80 pixels6400 pixels total
6.6x6.6 millidegrees28 pixels collectedBlack = no data
Scaled to show faint detail1.13 (h) x1.22 (w) degrees
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Pixel Time Series
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What Do Stars Sound Like?
HAT-P-7B Another Star
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Data Challenge Number 1
Dealing with Instrumental Systematic Errors
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Correcting Systematic Errors
CALPixel Level
Calibrations
PAPhotometricAnalysis
Sums Pixels Together/Measures Star Locations
TPSTransiting
PlanetSearch
RawData
TCEs: Threshold Crossing Events
CorrectedLight Curves
CalibratedPixels
RawLight
Curves/Centroids
DVData
Validation
Diagnostic
Metrics
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PDC Often Does a Good Job
Bayesian approaches look promising!
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PDC Often Over-Fits Variable Stars
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PDC Is Fundamentally Flawed
PDC co-trends against instrumental signatures using least squares (LS) approach
LS attempts to explain all of a given time series, not just the part the model can explain well
There is no way a simple LS fit can “put on the brakes”
PDC often trades bulk RMS for increased noise at short time scales
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A Bayesian Solution
Examine behavior of ensemble of stars responding to systematics Formulate prior probability distributions for model coefficients Maximize Posterior Distribution:
“A Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule.”
€
ˆ θ = argmaxθ
log p x c( )[ ] + log p c( )[ ]{ }Maximum Likelihood Prior PDF
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A Much Better Result
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PDC MAP Example
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PDC MAP Example 2
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Data Challenge Number 2
Detecting Weak Transits Against Non-White, Non-Stationary Noise
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Detecting Transiting Planets
CALPixel Level
Calibrations
PAPhotometricAnalysis
Sums Pixels Together/Measures Star Locations
TPSTransiting
PlanetSearch
RawData
TCEs: Threshold Crossing Events
CorrectedLight Curves
CalibratedPixels
RawLight
Curves/Centroids
DVData
Validation
Diagnostic
Metrics
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21
Matched Filtering: What Does This Mean?
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Detection StatisticsDefine
Under H0:
Under H1:
If T < , then choose H0, if T > , then choose H1
€
T =xT s
σ w sT s
€
T = 0, σ T2 =1
€
T = 1σ w
sT s, σ T2 =1
s
ws+w
TT
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Detection Statistics For Colored Noise
w is (colored) Gaussian noise with autocorrelation matrix Rx is the datas is the signal of interest
Decide s is present if
How do we determine R?
If the noise is stationary, we can work in the frequency domain:€
T =xT R−1s
sT R−1s=
Hx( )T
Hs( )
Hs( )T
Hs( )=
˜ x T ˜ s
˜ s T ˜ s >γ
€
T =X( f )S*( f )
P( f )df∫ S( f )S*( f )
P( f )∫ df
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Solar Variability
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PSDs for Solar-Like Variability
Is stellar variability stationary?
No!
We must work in a joint time-frequency domain
Wavelets are a natural choice
High Solar Activity
Low Solar Activity
Detect
able E
nergy
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A Wavelet-Based Approach
Filter-Bank Implementation of an Overcomplete Wavelet Transform The time series x(n) is partitioned (filtered) into complementary channels:
WX(i,n) = {h1(n) x(n), h2(n) x(n),…, hM(n) x(n)} = {x1(n), x2(n),…, xm(n)}
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A Wavelet-Based Approach
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Kepler-like Noise + Transits
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Single Transit Statistics
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Folded Transit Statistics
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Folded Statistics at Best-Matched Period
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Data Challenge Number 3
Excess Stellar Variability
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Image by Carter Roberts (1946-2008)
Excess Stellar VariabilityOriginal Noise Budget (Kp=12):
14 ppm Shot Noise10 ppm Instrument Noise10 ppm Stellar Variability
=> 20 ppm Total Noise
Reality (11.5 ≤ Kp ≤ 12.5)17 ppm Shot Noise13 ppm Instrument Noise20 ppm Stellar Variability
=> ~29 ppm Total Noise
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Original expectations yielded ~65% completeness for Earth analogs at 3.5 years
Completeness Vs. Time
Expected
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Current expectations yield <5% completeness for Earth analogs at 3.5 years
Expected Reality
Completeness Vs. Time
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~65% completeness for 1.2-Re planets in same orbits at 3.5 years
Expected Reality
Completeness Vs. Time
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Kepler will recover >60% completeness for Earth analogs after 8 years
Expected Reality
Completeness Vs. Time
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Completeness Vs. Time
20 ppm
30 ppm
Kepler will detect virtually all Venus analogs within 8 years
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Kepler is revolutionizing the field of exoplanets Kepler data are in a class of their own with
significant data challenges Huge dynamic range for measurements requires
sophisticated Bayesian techniques for correcting systematic errors
Planet detection requires an efficient, adaptive
Conclusions
method that accounts for non-white noise: wavelets fit the bill Kepler can reach its goal of detecting Earth-Sun analogs with an extended 8 year
mission Each day we are getting closer and closer to finding an Earth-Sun analog
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Image by Carter Roberts (1946-2008)
Music From the Stars
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Music From the Stars (2)
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Image by Carter Roberts (1946-2008)
Music From the Stars (3)
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Music From the Stars (4)
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