Data Challenges in Astronomy: NASA’s Kepler Mission and the Search for Extrasolar Earths

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

The Kepler Mission

What fraction of sun-like stars in our galaxy host potentially habitable Earth-size planets?

How Hard is it to Find Good Planets?

Earth or Venus0.01% area of the Sun (1/10,000)

Kepler Field Of View

Credit: Carter Roberts

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

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

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

Pixel Time Series

What Do Stars Sound Like?

HAT-P-7B Another Star

Data Challenge Number 1

Dealing with Instrumental Systematic Errors

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

PDC Often Does a Good Job

Bayesian approaches look promising!

PDC Often Over-Fits Variable Stars

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

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

A Much Better Result

PDC MAP Example

PDC MAP Example 2

Data Challenge Number 2

Detecting Weak Transits Against Non-White, Non-Stationary Noise

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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Matched Filtering: What Does This Mean?

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

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

Solar Variability

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

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)}

A Wavelet-Based Approach

Kepler-like Noise + Transits

Single Transit Statistics

Folded Transit Statistics

Folded Statistics at Best-Matched Period

Data Challenge Number 3

Excess Stellar Variability

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

Original expectations yielded ~65% completeness for Earth analogs at 3.5 years

Completeness Vs. Time

Expected

Current expectations yield <5% completeness for Earth analogs at 3.5 years

Expected Reality

Completeness Vs. Time

~65% completeness for 1.2-Re planets in same orbits at 3.5 years

Expected Reality

Completeness Vs. Time

Kepler will recover >60% completeness for Earth analogs after 8 years

Expected Reality

Completeness Vs. Time

Completeness Vs. Time

20 ppm

30 ppm

Kepler will detect virtually all Venus analogs within 8 years

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

Image by Carter Roberts (1946-2008)

Music From the Stars

Image by Carter Roberts (1946-2008)

Music From the Stars (2)

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Image by Carter Roberts (1946-2008)

Music From the Stars (3)

42

Image by Carter Roberts (1946-2008)

Music From the Stars (4)

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