PSF Photometry for Kepler/K2 data Geert Barentsen Z´ e Vin´ ıcius http://keplerscience.arc.nasa.gov Space Telescope Science Institute, Baltimore November 6, 2017 

K2 Guest Observer Office + Ben Montet Geert Barentsen Michael Gully Ann Marie Cody Christina Hedges Z´ e Vin´ ıcius Ben Montet 1 

PSF Photometry of Multiple Overlapping Stars 2 

PSF Photometry of Multiple Overlapping Stars • Data: single image, time-series of images, etc... 2 

PSF Photometry of Multiple Overlapping Stars • Data: single image, time-series of images, etc... • Parameters: θ(1) = x(1) 0 , y(1) 0 , F(1), B ... θ(K) = x(K) 0 , y(K) 0 , F(K), B That’s a total of 3K + 1 parameters! 2 

PSF Photometry of Multiple Overlapping Stars • Data: single image, time-series of images, etc... • Parameters: θ(1) = x(1) 0 , y(1) 0 , F(1), B ... θ(K) = x(K) 0 , y(K) 0 , F(K), B That’s a total of 3K + 1 parameters! • Model: PSF x, y, θ(k) = F(k)h x − x(k), y − y(k) + B K 2 

PSF Photometry of Multiple Overlapping Stars • Data: single image, time-series of images, etc... • Parameters: θ(1) = x(1) 0 , y(1) 0 , F(1), B ... θ(K) = x(K) 0 , y(K) 0 , F(K), B That’s a total of 3K + 1 parameters! • Model: PSF x, y, θ(k) = F(k)h x − x(k), y − y(k) + B K • Objective: θ = arg min θ∈Θ x,y dataxy − k PSF x, y, θ(k) 2 2 

DAOPHOT-like PSF Photometry stars = find(image) // DAOFIND 3 

DAOPHOT-like PSF Photometry stars = find(image) // DAOFIND while len(stars) > 0: groups = group(stars) // DBSCAN 3 

DAOPHOT-like PSF Photometry stars = find(image) // DAOFIND while len(stars) > 0: groups = group(stars) // DBSCAN fitted_groups = fit(groups, model) 3 

DAOPHOT-like PSF Photometry stars = find(image) // DAOFIND while len(stars) > 0: groups = group(stars) // DBSCAN fitted_groups = fit(groups, model) residual = subtract(image, fitted_groups) 3 

DAOPHOT-like PSF Photometry stars = find(image) // DAOFIND while len(stars) > 0: groups = group(stars) // DBSCAN fitted_groups = fit(groups, model) residual = subtract(image, fitted_groups) stars = find(residual) 3 

DAOPHOT-like PSF Photometry stars = find(image) // DAOFIND while len(stars) > 0: groups = group(stars) // DBSCAN fitted_groups = fit(groups, model) residual = subtract(image, fitted_groups) stars = find(residual) 3 

How are we doing PSF Photometry? K2 data looks like: 4 

How are we doing PSF Photometry? K2 data looks like: 4 

The Kepler Pixel Response Function Our module looks like: 5 

Our tools: PyKE and oktopus PyKE: KeplerPRF, KeplerTargetPixelFile, KeplerPRFPhotometry (work in progress) pyke.keplerscience.org 6 

Our tools: PyKE and oktopus oktopus: Likelihood, Prior, Posterior keplergo.github.io/oktopus 7 

Fitting K2 data 8