Searching for Galaxy Cluster-Scale Strong lenses from the DESI Legacy Imaging Surveys

Abstract

Galaxy cluster-scale strong gravitational lensing systems are rare yet valuable tools for investigating the properties of dark matter and dark energy, as well as providing the opportunity to study the distant universe at flux levels and spatial resolutions that would otherwise be unavailable. Large-scale imaging surveys present unprecedented opportunities to expand the sample of cluster lenses. In this study, we adopt a deep learning-based approach to identify cluster lenses from the DESI Legacy Imaging Surveys, utilizing the catalog of galaxy cluster candidates identified by Zou et al. (2021). Our lens-finder employs a ResNet-18 architecture, trained with mock images of cluster lenses as positives and observational images of cluster scale non-lenses as negatives. We do an iterative operation to increase the completeness of our work, namely adding the found true positive samples back to the training set and training again for several times. Human inspection is conducted to further refine the candidates, categorizing them into grades (A, B, C) according to the significance of the strongly lensed arcs. Reviewing all 540,432 objects in Zou's catalog, we discover 485 high-confidence cluster lens candidates with a cluster $M_{500}$ range of $10^{13.67\sim14.97}M_{\odot}$ and a Brightest Central Galaxy (BCG) redshift range of $0.04\sim0.89$. After excluding the lens candidates listed in previous studies, we identify 247 newly discovered cluster lens candidates, including 16 grade A, 90 grade B, and 141 grade C. This catalog of cluster lens candidates is publicly available online, and follow-up observations are encouraged to confirm and conduct thorough investigations of these systems.

Figures (13)

• Figure 1: One example for our mock program, with side length of $100"$. Left: One selected non-lensed cluster image. Middle: The mock arc image to be added to the cluster image, together with the critical curves (red curve) and the caustics (green curve). The orange crosses indicate the positions of the member galaxies within the galaxy cluster, while the cyan cross indicate the source position. Right: The final mock lensing images.
• Figure 2: Distributions for parameters without analytic forms in Table \ref{['tab:mock_parameter']}. The source effective radius is units of arcseconds.
• Figure 3: UMAP projection of randomly selected 800 mock lenses from the training set, including the systems with red (blue star), green (blue cross), and blue (blue diamond) sources defined in our manuscript (See Section \ref{['subsec: mock']}). Red dots present the UMAP of 177 cluster-scale strong lenses from the COOL-LAMPS project 2025ApJ...979..184M.
• Figure 4: Left: The cross-entropy loss on the training and validation sets over 200 training epochs with two cases in the final iteration of our training. In Case 1, we adopt Adam optimizer, configured with a batch size of 32, a learning rate of $3\times10^{-6}$, and a weight decay of $1\times10^{-1}$. Moreover, in Case 2, We use a initial learning rate of $1\times10^{-4}$, a final learning rate of $1\times10^{-5}$, a weight decay of $1\times10^{-2}$ , with Cosine Annealing. The vertical dashed line at epoch 20 and 90 indicates the early stopping points we selected in the two cases, which is the highest point of the AUC (Case 2), or the highest AUC before the training loss become abnormal (Case 1). Middle: The Area Under the ROC curve as a function of epoch in the same training session. Right: The derivative of AUC as a function of epoch in the same training session.
• Figure 5: Comparison of the performance of our classifier evaluated with validation and testing sets separately. The left panel shows the ROC curve (orange line) of our classifier on the validation set containing our mock images with the area under the curve (AUC=0.939). And the ROC curve (blue line) of our classifier on the testing set containing the lens candidates from the COOL-LAMPS project 2025ApJ...979..184M with the area under the curve (AUC=0.722). The right panel shows the PR curve for the above two cases. We also mark the threshold (0.986) adopted in last iteration with red stars.