Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.