Detection of Transiting Planet Candidates in Kepler Mission Data

Transcription

1 Detection of Transiting Planet Candidates in Kepler Mission Data Peter Tenenbaum For the Kepler Transiting Planet Search Team 2012-June-06 SAO STScI!

2 The Kepler Mission A space-based photometer searching for Earth-size exoplanets Uses transit photometry monitors ~150,000 stars almost continuously for 3 or more years looking for periodic dips in intensity (actually total dataset includes > 190,000 stars) Huge field of view (115 square degrees) 96 megapixels on focal plane in 42 CCDs (84 readout channels total) Launched into earth-trailing heliocentric orbit on March 6, 2009

3 Kepler Data and Processing Kepler records intensity of selected pixels on 29.4 minute cadence pixels selected on ground, commanded to spacecraft Spacecraft rolls about telescope axis every 93 days ( quarter ) keeps solar panels pointed at Sun A given star is imaged on 4 different CCDs over the course of a 372-day Kepler year Transiting Planet Search (TPS) module combines light curves from individual quarters and searches

4 TPS: Setting the Scale Transit of an exo-earth orbiting an exo-sol is ~13 hour event, once per 365 days, with 100 PPM max depth A transit candidate is defined by 3 events necessary to ensure true periodicity So the scale of the problem is: Search 190,000 stars which are sampled every 30 minutes for several years for a periodic 100 PPM dip in intensity against the background of stellar variability There s a 300 PPM transit signal in this light curve. Good luck seeing it.

5 TPS: Key Issues False detection rejection False detections è excessive computational load in DV + excessive vetting effort True detection retention True detections expected to be a few % of all targets due to inclination angle alignments Don t want false detection removal to accidentally take out any true detections Throughput 190,000 x anything = big number

6 Step 1: Whitening the Light Curve Stellar variability highly non-white and nonstationery Need joint timefrequency approach to remove Wavelet-based digital filter bank DSP version of your home stereo s graphic equalizer Converts light curve to white noise + impulsive outliers (like transits) Sample light curve with transits before whitening (top) and after (bottom).

7 Whitening Light Curves (2) Whitening process distorts shape of transit Distortion varies in time because noise content in light curve varies Searching for timevarying signal against background of white noise Unwhitened (left) and whitened (right) transit from the example on the previous slide, showing the change in shape of the transit due to whitening.

8 Searching for Transits (1) Step 1: search for individual transits Correlate whitened flux against distorted square model transit pulse 14 different transit durations used, from 1.5 hours to 15 hours Produces signal time series and noise time series Ratio of these is the Single Event Statistic (SES) time series

9 Searching for Transits (2) Step 2: fold the statistics at selected periods and phases to form the Multiple Event Statistic (MES) Folding time scales roughly as square of time series length Identify the period / phase combination which produces maximum MES

10 Thresholding Every target has some combination of period and phase which is the max MES for that target Duh Need to set a threshold which cuts off MES values which are due to chance alignments of noise Pre-launch study: 7.1 σ threshold would limit statistical false positives to 1 per mission Exo-Earth with 3 transits of 4.1 σ would be found Expected noise for Sun-like stars was ~20 PPM Exo-Earth transit ~100 PPM So no problem, or so we thought

11 What Actually Happened ~86,000 targets with MES > 7.1 σ Clearly dominated by false alarms What happened? Spacecraft environment very different from original understanding Results in the strong features in the wedge plot Detection statistics of individual targets have long non-gaussian tails TPS folding doesn t check to make sure that the statistics which go into a MES are sensible 1 very strong event + noise often yields 7.1 σ

12 Reducing False Alarms Addition of robust statistic (RS) Robust fit of model transit to period / phase of MES Helps to identify cases with highly unequal events Reduces # of detections to ~25,000 Some features removed, others remain RS has similar weaknesses to MES, ie, can be spoofed by mixture of strong event + weak events

13 Reducing False Alarms (2) Use relationships among SES, MES, RS Ie, take advantage of the fact that most false alarms have 1 strong event Originally looked at MES/ SES Later moved to RS * MES / SES More effective at identifying false alarms Less strong theoretical basis, more empirical Combining MES, RS, and ratio yields 11,800 detections Acceptable for now

14 Execution Time TPS is almost all MATLAB m- files Folder is C-language mexfile with multi-thread capability Runtime Dominated by folding process Somewhat non-deterministic RS algorithm can remove some samples and rerun folder Times acceptable for now Runs on NASA Ames But n 2 scaling is brutal 8 year mission implies that some targets will take > 70 hours! Even typical targets will take 2.5 hours NB: Data validation (DV) software uses TPS to look for multiple planets in a system DV runtime also critically depends on TPS

15 Future Developments Current search logic is inadequate If statistic ratio test indicates false detection, search exits What if there s a weak real signal buried beneath a strong spurious one? Need the ability to go back to the data and examine weaker signals until all possible detections exhausted Statistically likely that we will accept more false alarms this way Hopefully also dig out more true detections Care required to maintain adequate execution speed, since in principle we can wind up looping over a lot of possible detections

16 Future Developments (2) Statistic ratio test always been somewhat ad hoc Testing a better method for identifying false alarms based on wildly unequal signals Directly examines shape and depth of the transits in a detection to see that they are consistent within expected variation Uses time-frequency decomposition algorithm described earlier Much better and more theoretically sound algorithm Execution speed acceptable

17 Future Developments (3) Throughput will continue to be a challenge as data volume increases Do not expect NASA supercomputer capacity to keep up Shipping huge volumes of data to NAS and back also challenging It s a supercomputer, not a supernetwork! A few things we can do cheaply to beat CPU time down Research on a faster algorithm will be necessary

18 TPS Team Chris Burke, Jessie Christiansen, Jon Jenkins, Sean McAullife, Shawn Seader, PT, Joe Twicken