Extracting the Subhalo Mass Function from Strong Lens Images with Image Segmentation

TL;DR

This paper introduces a machine learning approach using image segmentation to detect and measure subhalos in strong lens images, enabling efficient estimation of the subhalo mass function without detailed lens modeling.

Contribution

The authors develop a neural network that locates subhalos and estimates their mass directly from images, bypassing traditional modeling and source reconstruction methods.

Findings

Detects subhalos with masses > 10^{8.5} M_{ ext{sun}}.

Achieves a false-positive rate of about three per 100 images.

Recovers the subhalo mass function slope with 36% error using 50 images, improving to 10% with 1000 images.

Abstract

Detecting substructure within strongly lensed images is a promising route to shed light on the nature of dark matter. However, it is a challenging task, which traditionally requires detailed lens modeling and source reconstruction, taking weeks to analyze each system. We use machine-learning to circumvent the need for lens and source modeling and develop a neural network to both locate subhalos in an image as well as determine their mass using the technique of image segmentation. The network is trained on images with a single subhalo located near the Einstein ring across a wide range of apparent source magnitudes. The network is then able to resolve subhalos with masses $m\gtrsim 10^{8.5} M_{\odot}$. Training in this way allows the network to learn the gravitational lensing of light, and remarkably, it is then able to detect entire populations of substructure, even for locations further away from the Einstein ring than those used in training. Over a wide range of the apparent source magnitude, the false-positive rate is around three false subhalos per 100 images, coming mostly from the lightest detectable subhalo for that signal-to-noise ratio. With good accuracy and a low false-positive rate, counting the number of pixels assigned to each subhalo class over multiple images allows for a measurement of the subhalo mass function (SMF). When measured over three mass bins from $10^9M_{\odot}$--$10^{10} M_{\odot}$ the SMF slope is recovered with an error of 36% for 50 images, and this improves to 10% for 1000 images with Hubble Space Telescope-like noise.