Detection and Characterization of Exoplanets using Projections on Karhunen-Loeve Eigenimages: Forward Modeling

Abstract

A new class of high-contrast image analysis algorithms that empirically fit and subtract systematic noise has lead to recent discoveries of faint exoplanet /substellar companions and scattered light images of circumstellar disks. These methods are extremely efficient at enhancing the detectability of faint astrophysical signal, but they do generally create systematic biases in their observed properties. This paper provides a general solution for this outstanding problem. We present the analytical derivation of a linear expansion that captures the impact of astrophysical over-subtraction and/or self-subtraction these image analysis techniques. We examine the general case for which the reference images of the astrophysical scene move azimuthally and/or radially across the field of view as a result of the observation strategy. Our new method is based on perturbing the covariance matrix underlying any least-squares speckles problem, and propagating this perturbation through the data analysis algorithm. We then demonstrate practical applications of this new algorithm. We first consider the case of the spectral extraction of faint point sources in IFS data and illustrate, using public Gemini Planet Imager commissioning data, that our novel perturbation-based Karhunen-Lo\`eve Image Processing Forward Modeling (KLIP-FM) can indeed alleviate algorithmic biases. We then apply KLIP-FM to the problem associated with the detection of point sources. We show how it decreases the rate of false negatives (e.g missed planets) while keeping the rate of false positives unchanged when compared to classical least-squares fitting methods. This can potentially have important consequences on the design of follow-up strategies of ongoing direct imaging surveys.