Polar coordinate transformations for machine learning based dark matter subhalo detection in strong gravitational lenses

Abstract

Strong gravitational lensing provides a powerful probe of dark matter, particularly on small scales where the gravitational effects of dark matter subhalos within galaxies can manifest as perturbations within the extended arcs of gravitationally lensed sources. We investigate whether transforming lensed images into polar coordinates improves the ability of convolutional neural networks to infer subhalo mass. We introduce a machine learning architecture that outputs a prediction uncertainty alongside a mass prediction to enable assessment of network reliability. Using simulated Hubble Space Telescope observations, we compare our models trained on Cartesian and polar representations under different initialisation schemes, noise levels, and subhalo concentrations ($c=60$, $c=30$). We find that polar-transformed inputs consistently yield higher subhalo detection fractions than standard Cartesian images across all tested masses. For subhalos with mass $10^9M_\odot \leq M \leq 10^{9.5}M_\odot$, the fraction of subhalos the network is able to detect increases by $\sim 15$ per cent. Pretrained networks outperform randomly initialized networks, and the polar transform consistently improves network performance in both low signal-to-noise data and for lower-concentration subhalos. The relative improvement is highest in regimes where subhalo perturbations are most difficult to detect, such as low signal-to-noise data or systems containing low concentration subhalos. These results demonstrate that presenting strong lensing images in a polar representaion provides a computationally inexpensive way of improving CNN-based subhalo detection.