A PCA-based automated finder for galaxy-scale strong lenses

¹ Laboratoire d’Astrophysique, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
e-mail: frederic.courbin@epfl.ch
² Dipartimento di Fisica e Astronomia – Universita di Bologna, via Berti Pichat 6/2, 40127 Bologna, Italy
³ INAF – Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
⁴ INFN – Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵ Jodrell Bank Centre for Astrophysics, School of Physics & Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁶ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
⁷ Department of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 München, Germany
⁸ Jet Propulsion Laboratory, 4800 Oak Grove Dr., La Canada-Flintridge CA 91011, USA
⁹ Max-Planck-Institut für Astrophysik, 85748 Garching, Germany
¹⁰ Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching, Germany
¹¹ Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/SEDI-SAP, Service d’Astrophysique, CEA Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France

Received: 1 January 2014
Accepted: 14 February 2014

Abstract

We present an algorithm using principal component analysis (PCA) to subtract galaxies from imaging data and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is optimised to find full or partial Einstein rings. Starting from a pre-selection of potential massive galaxies, we first perform a PCA to build a set of basis vectors. The galaxy images are reconstructed using the PCA basis and subtracted from the data. We then filter the residual image with two different methods. The first uses a curvelet (curved wavelets) filter of the residual images to enhance any curved/ring feature. The resulting image is transformed in polar coordinates, centred on the lens galaxy. In these coordinates, a ring is turned into a line, allowing us to detect very faint rings by taking advantage of the integrated signal-to-noise in the ring (a line in polar coordinates). The second way of analysing the PCA-subtracted images identifies structures in the residual images and assesses whether they are lensed images according to their orientation, multiplicity, and elongation. We applied the two methods to a sample of simulated Einstein rings as they would be observed with the ESA Euclid satellite in the VIS band. The polar coordinate transform allowed us to reach a completeness of 90% for a purity of 86%, as soon as the signal-to-noise integrated in the ring was higher than 30 and almost independent of the size of the Einstein ring. Finally, we show with real data that our PCA-based galaxy subtraction scheme performs better than traditional subtraction based on model fitting to the data. Our algorithm can be developed and improved further using machine learning and dictionary learning methods, which would extend the capabilities of the method to more complex and diverse galaxy shapes.