docLecture 3: Ensemble photometry and transit detection
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Lecture 3: Ensemble photometry and transit detection
Lecture 3: Ensemble photometry and transit detection! Ensemble differential photometry! Systematics and decorrelation methods! Transit detection by box least-squares! Noise and completeness! Vietri Sul Mare 2015! The Transit Method! Detrending – the PyKE way! http://keplerscience.arc.nasa.gov/PyKE.shtml! Vietri Sul Mare 2015! The Transit Method! Kepler SAP and PDC-SAP! Simple Aperture Photometry (SAP)! Pre-search Data Conditioning (PDC)! http://keplerscience.arc.nasa.gov/DataAnalysisProducts.shtml! Vietri Sul Mare 2015! The Transit Method! WASP data reduction pipeline! Flatfield Bias Preprocessed Raw Dark Current Exposur e Map 16h43+31d26 field 2004 May-Aug 1 Flux-RMS RMS scatter (mag) 0.1 Series1 Field recognition, astrometry, aperture photometry, calibration/ de-trending 0.01 12 Sul Mare 2015! Vietri 0.001 9 10 11 12 WASP V magnitude 13 14 The Transit Method! Catalogue-driven photometry! • Step 1: Object detection! – e.g (S)EXTRACTOR! – Catalogue all objects on frame to detection threshold! • Step 2: Establish astrometric solution! – Many standard algorithms available, e.g. astrometry.net! – Cross-match with astrometric catalogue! – Write world coordinate system to image.! • Step 3: Aperture photometry! – Optimise aperture – many ways to do this!! – Use frame catalogue to exclude faint objects in sky annulus! Vietri Sul Mare 2015! The Transit Method! Ensemble differential photometry! • Mean magnitude of star j:! Additional intra-frame variance! (downgrades poor images)! • Zero-point correction for frame i:! Vietri Sul Mare 2015! Additional stellar variance! (downgrades variable objects)! ! The Transit Method! Frame quality and stellar variability I! • Define data vector X and model µ: ! ! • Assuming Gaussian errors:! ! • Likelihood of entire data vector for star j:! • Where:! Vietri Sul Mare 2015! The Transit Method! Frame quality and stellar variability II! • Maximise likelihood w.r.t. σ2s(j) and σ2t(i):! – Solve iteratively for σ2s(j) holding σ2t(i) constant:! – Solve iteratively for σ2t(i) holding σ2s(j) constant:! ! ^! ^! 2 2 • Iterate m j, zi, σ s(j) and σ t(i) to convergence.! Vietri Sul Mare 2015! The Transit Method! Decorrelation/ systematics removal! Tamuz et al 2005! 16h30+28 field 300 stars 2549 observations 100 days 782 903 Aspen 2005! Vietri Sul Mare 2015! The Transit Method! Systematics and correlated noise! • References:! – – – – – Tamuz, Mazeh & Zucker 2005, MNRAS 355, 1466 (SysRem)! Kovacs, Bakos & Noyes 2005, MNRAS 356, 537 (TFA)! Pont, Zucker & Queloz 2006, MNRAS 373, 231! Carter & Winn 2009, ApJ 704, 51! Gibson 2014, MNRAS 445, 3401! Vietri Sul Mare 2015! The Transit Method! SysRem! • Many patterns of systematics are common to all stars! – Secondary extinction: dependence on stellar colour! – Sky brightness: Dependence on target brightness! – Ambient temperature and focus drift: position dependent?! • SysRem: PCA with error bars!! – Construct common temporal basis functions! – Compute optimal scaling coefficient per star! – Remove and repeat.! Vietri Sul Mare 2015! The Transit Method! SysRem algorithm! • SysRem produces a corrected magnitude given by:! • Search for the best cj that minimises:! X (k 1) 2 Si = ((k 1) x̃i,j (k) ci (k) aj )2 wi,j i,j (k) cj = X (k 1) j Vietri Sul Mare 2015! 1) ai wi,j (k 1) a2 w i i,j i • Similarly! X (k (k) ai = x̃i,j (k 1) x̃i,j (k 1) cj wi,j (k 1) c2 w j i,j The Transit Method! SysRem basis functions vs HA! 0.05 0.04 0.06 0.03 ai . <(2)cj2>1/2 (magnitude) 0.08 0.04 0.02 0 -0.02 -0.04 (2) (1) ai . <(1)cj2>1/2 (magnitude) 0.1 0 -0.01 -0.02 -0.03 -0.08 -0.04 -0.05 -4 -3 -2 -1 0 1 2 3 4 -4 Hour Angle 0.05 -3 -2 -1 0.04 0.03 0.03 ai . <(4)cj2>1/2 (magnitude) 0.04 0.02 0.01 0 -0.01 -0.02 1 2 3 4 1 2 3 4 0.02 0.01 0 -0.01 -0.02 -0.03 -0.03 -0.04 -0.04 -0.05 0 Hour Angle 0.05 (4) ai . <(3)cj2>1/2 (magnitude) 0.01 -0.06 -0.1 (3) 0.02 -0.05 -4 -3 -2 -1 Vietri Sul Mare 2015! 0 Hour Angle 1 2 3 4 -4 -3 -2 -1 0 The Transit Method! Hour Angle Decorrelation/ systematics removal! Tamuz et al 2005! 16h30+28 field 300 stars 2549 observations 100 days 782 Vietri Sul Mare 2015! 903 The Transit Method! Decorrelation/ systematics removal! Tamuz et al 2005! 16h30+28 field 300 stars 2549 observations 100 days 782 Vietri Sul Mare 2015! 903 The Transit Method! Decorrelation & Detection! • Decorrelation:! – 4-stage SysRem! – TFA with reconstruction! • Detection: Cameron et al 2006 MNRAS 373, 799 ! – Accelerated BLS algorithm! – Coarse grid search ! – Newton-Raphson peak-up on 5 strongest peaks! – Box width varies with period! • Example: WASP-1! Vietri Sul Mare 2015! The Transit Method! Box Least-Squares transit search! • References! – Kovacs, Zucker & Mazeh 2002, A&A 391, 369! – Aigrain & Irwin 2004, MNRAS 350, 331! – Collier Cameron et al 2006, MNRAS 373, 799! • Step 1: Compute inverse variance-weighted mean flux, subtract and precompute χ20, t :! • Step 2: set up frequency grid! – phase of each observation must change by less than transit duration between adjacent frequencies! • Step 3: estimate range of transit duration! – Use stellar density! Vietri Sul Mare 2015! The Transit Method! Box Least-Squares transit search! • Step 3: Phase-fold and partition:! – Mean light level in-transit (L):! – Mean light level out of transit (H):! – Fitted transit depth (δ):! Vietri Sul Mare 2015! The Transit Method! Box Least-Squares transit search! • Step 4: Badness-of-fit:! – Signal-to-noise ratio of transit depth! – Improvement in fit relative to constant model is (S/N)2:! – Goodness of fit outside transit:! Vietri Sul Mare 2015! The Transit Method! Box Least-Squares transit search! • Step 5: BLS periodogram! Vietri Sul Mare 2015! The Transit Method! Box Least-Squares transit search! • Step 5: BLS periodogram! Vietri Sul Mare 2015! The Transit Method! Planet search! • SysRem+BLS! • Tamuz, Mazeh & Zucker 2005! • Kovacs, Zucker & Mazeh 2002! Vietri Sul Mare 2015! • Skype-linked network of human neuro-visual processors.! • Each processor allocated several thousand candidate light curves + associated statistics from main database.! • Motivated by promises of food, postdoc employment, fame, glory, etc.! The Transit Method! Systematics and red noise! RMS scatter! RMS scatter (real data, 2.5-hr bins)! RMS scatter (white noise, 2.5-hr bins)! • Systematics:! – Secondary extinction! – Temperature-dependent focus! – Sky brightness-dependent bias in background subtraction! – SysRem: Tamuz et al 2005! – TFA: Kovacs et al 2005! • Red noise:! – Pont et al 2006! – Smith et al 2006! Vietri Sul Mare 2015! RMS scatter! RMS scatter (real data, 2.5-hr bins)! RMS scatter (white noise, 2.5-hr bins)! The Transit Method! Red noise and detection threshold! Smith, A M S et al, 2006! 80 nights! 80 nights! 130 nights! 130 nights! Vietri Sul Mare 2015! The Transit Method! Red noise and planet catch! Season 1! Season 2! Vietri Sul Mare 2015! The Transit Method! Summary! • Systematics and astrophysical variability mask transits! • Not all systematics are understood! • PCA-like methods (e.g. SysRem, PDC-MAP) remove systematics while preserving astrophysical variability! • More aggressive detrending (e.g. TFA) removes astrophysical variability too! • Box least-squares method is efficient! • Correlated noise must be taken into account when assessing detection thresholds.! Vietri Sul Mare 2015! The Transit Method!
![arXiv:1602.05957v2 [astro-ph.GA] 8 Aug 2016](http://s1.doczz.it/store/data/000139930_1-813332864f26c1ce388c9af0dada74f2-70x70.png "arXiv:1602.05957v2 [astro-ph.GA] 8 Aug 2016")