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

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

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

5. Kepler Field Of View Credit: Carter Roberts

6. 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  ~100×10 6 tests per star for planetary signatures [O(N 2 )]  Stellar variations are higher than expected Big Data:  >150,000 target stars  6x10 6 pixels collected and stored per ½ hour  ~40 GB downlinked each month  >40×10 9 points in the time series over 3.5 years

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

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

9. Pixel Time Series

10. What Do Stars Sound Like? HAT-P-7BAnother Star

11. Data Challenge Number 1 Dealing with Instrumental Systematic Errors

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

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

14. PDC Often Over-Fits Variable Stars

15. 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

16. 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.” Maximum LikelihoodPrior PDF

17. A Much Better Result

18. PDC MAP Example

19. PDC MAP Example 2

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

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

22. 21 Matched Filtering: What Does This Mean?

23. Detection Statistics Define Under H0: Under H1: If T , then choose H1 s w s+w TT

24. 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 s is present if How do we determine R? If the noise is stationary, we can work in the frequency domain:

25. Solar Variability

26. 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

27. A Wavelet-Based Approach Filter-Bank Implementation of an Overcomplete Wavelet Transform The time series x(n) is partitioned (filtered) into complementary channels: W X (i,n) = {h 1 (n)  x(n), h 2 (n)  x(n),…, h M (n)  x(n)} = {x 1 (n), x 2 (n),…, x m (n)}

28. A Wavelet-Based Approach

29. Kepler-like Noise + Transits

30. Single Transit Statistics

31. Folded Transit Statistics

32. Folded Statistics at Best-Matched Period

33. Data Challenge Number 3 Excess Stellar Variability

34. Image by Carter Roberts (1946-2008) 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

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

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

37. ~65% completeness for 1.2-R e planets in same orbits at 3.5 years Expected Reality Completeness Vs. Time

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

39. 20 ppm 30 ppm Kepler will detect virtually all Venus analogs within 8 years

40.  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

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

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

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

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