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

1. SAO Data Challenges in Astronomy: NASA’s Kepler Mission and the Search for Extrasolar Earths STScI • Jon M. Jenkins • SETI Institute/NASA Ames Research Center • Thursday September 22, 2011

2. The Kepler Mission What fraction of sun-like stars in our galaxy host potentially habitable Earth-size planets?

3. How Hard is it to Find Good Planets? Earth or Venus 0.01% area of the Sun (1/10,000) Jupiter 1% area of the Sun (1/100)

4. Kepler Field Of View Credit: Carter Roberts

5. Kepler: Big Data, Big Challenges 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 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

6. The Kepler Science Pipeline: From Pixels To Planets PA Photometric Analysis Sums Pixels Together/Measures Star Locations PA Photometric Analysis Sums Pixels Together/Measures Star Locations Calibrated Pixels CAL Pixel Level Calibrations CAL Pixel Level Calibrations Raw Data Raw Light Curves/ Centroids PDC Pre-Search Data Conditioning Removes Systematic Errors PDC Pre-Search Data Conditioning Removes Systematic Errors Corrected Light Curves TPS Transiting Planet Search TPS Transiting Planet Search DV Data Validation DV Data Validation Diagnostic Metrics TCEs: Threshold Crossing Events

7. Image Data HAT-P-7b pixels 6.6x6.6 millidegrees 28 pixels collected Black = no data 0.09x0.09 degrees 80x80 pixels 6400 pixels total Scaled to show faint detail 1.13 (h) x1.22 (w) degrees

8. Pixel Time Series

9. What Do Stars Sound Like? HAT-P-7B Another Star

10. Data Challenge Number 1 Dealing with Instrumental Systematic Errors

11. Correcting Systematic Errors PA Photometric Analysis Sums Pixels Together/Measures Star Locations Calibrated Pixels CAL Pixel Level Calibrations Raw Data Raw Light Curves/ Centroids PDC Pre-Search Data Conditioning Removes Systematic Errors Corrected Light Curves TPS Transiting Planet Search DV Data Validation Diagnostic Metrics TCEs: Threshold Crossing Events

12. PDC Often Does a Good Job Bayesian approaches look promising!

13. PDC Often Over-Fits Variable Stars

14. 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

15. A Bayesian Solution • Examine behavior of ensemble of stars responding to systematics • Formulate prior probability distributions for model coefficients • Maximize Posterior Distribution: Maximum Likelihood Prior PDF “A Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule.”

16. A Much Better Result

17. PDC MAP Example

18. PDC MAP Example 2

19. Data Challenge Number 2 Detecting Weak Transits Against Non-White, Non-Stationary Noise

20. Detecting Transiting Planets PA Photometric Analysis Sums Pixels Together/Measures Star Locations Calibrated Pixels CAL Pixel Level Calibrations Raw Data Raw Light Curves/ Centroids PDC Pre-Search Data Conditioning Removes Systematic Errors Corrected Light Curves TPS Transiting Planet Search DV Data Validation Diagnostic Metrics TCEs: Threshold Crossing Events

21. Matched Filtering: What Does This Mean? MATCH! NO MATCH! 21

22. Detection Statistics Define Under H0: Under H1: If T < g, then choose H0, if T > g, then choose H1 s+w w s T T

23. Detection Statistics For Colored Noise w is (colored) Gaussian noise with autocorrelation matrix R x is the data s is the signal of interest Decide sis present if How do we determine R? If the noise is stationary, we can work in the frequency domain: Looks like a simple matched filter!

24. Solar Variability

25. 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 Detectable Energy

26. 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)}

27. A Wavelet-Based Approach

28. Kepler-like Noise + Transits

29. Single Transit Statistics

30. Folded Transit Statistics

31. Folded Statistics at Best-Matched Period

32. Data Challenge Number 3 Excess Stellar Variability

33. Excess Stellar Variability Original Noise Budget (Kp=12): 14 ppm Shot Noise 10 ppm Instrument Noise 10 ppm Stellar Variability => 20 ppm Total Noise Reality (11.5 ≤ Kp ≤ 12.5) 17 ppm Shot Noise 13 ppm Instrument Noise 20 ppm Stellar Variability => ~29 ppm Total Noise Image by Carter Roberts (1946-2008)

34. Completeness Vs. Time Original expectations yielded ~65% completeness for Earth analogs at 3.5 years Expected

35. Completeness Vs. Time Current expectations yield <5% completeness for Earth analogs at 3.5 years Expected Reality

36. Completeness Vs. Time ~65% completeness for 1.2-Re planets in same orbits at 3.5 years Expected Reality

37. Completeness Vs. Time Kepler will recover >60% completeness for Earth analogs after 8 years Expected Reality

38. Completeness Vs. Time Kepler will detect virtually all Venus analogs within 8 years 30 ppm 20 ppm

39. Conclusions • 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 • 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

40. Music From the Stars Image by Carter Roberts (1946-2008)

41. Music From the Stars (2) Image by Carter Roberts (1946-2008) 41

42. Music From the Stars (3) Image by Carter Roberts (1946-2008) 42

43. Music From the Stars (4) Image by Carter Roberts (1946-2008) 43