A Search for Earth-size Planets

STScI!SAO

Detection of Transiting Planet Candidates in Kepler Mission Data

Peter Tenenbaum For the Kepler Transiting Planet Search Team

2012-June-06

A Search for Earth-size Planets 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)

Launched into earth-trailing heliocentric orbit on March 6, 2009

Huge field of view (115 square degrees) 96 megapixels on focal plane in 42 CCDs (84 readout channels total)

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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.

A Search for Earth-size Planets 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

A Search for Earth-size Planets

Step 1: Whitening the Light Curve

•  Stellar variability highly non-white and non-stationery –  Need joint time-

frequency 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).

A Search for Earth-size Planets Whitening Light Curves (2)

•  Whitening process distorts shape of transit –  Distortion varies in

time because noise content in light curve varies

•  Searching for time-varying 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.

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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…

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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 supercomputer

@ Ames •  But n2 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

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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

A Search for Earth-size Planets 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

A Search for Earth-size Planets TPS Team

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