HOLISMOKES. XIII. Strong-lens candidates at all mass scales and their environments from the Hyper-Suprime Cam and deep learning

We performed a systematic search for strong gravitational lenses using Hyper Suprime-Cam (HSC) imaging data, focusing on galaxy-scale lenses combined with an environment analysis resulting in the identification of lensing clusters. To identify these lens candidates, we exploited our residual neural network from HOLISMOKES VI, trained on realistic $gri$ mock-images as positive examples, and real HSC images as negative examples. Compared to our previous work, where we successfully applied the classifier to around 62.5 million galaxies having an $i$-Kron radius of $ we now lowered the $i$-Kron radius limit to $ The result in an increase by around 73 million sources, amounting to a total of over 135 million images. During our visual multi-stage grading of the network candidates, we also simultaneously inspected larger stamps ($80 to identify large, extended arcs cropped in the $10 cutouts and also classify their overall environment. Here, we also re-inspected our previous lens candidates with $i$-Kron radii of $ and classified their environment. Using the 546 visually identified lens candidates, we further defined various criteria by exploiting extensive and complementary photometric redshift catalogs to select the candidates in overdensities. In total, we identified grade A and grade B exhibit either spatially-resolved multiple images or extended, distorted arcs in the new sample. Furthermore, combining our different techniques to determine overdensities, we identified a total 231/546 lens candidates by at least one of our three identification methods for overdensities. This new sample contains only 49 group- or cluster-scale re-discoveries, while 43 systems had been identified by all three procedures. Furthermore, we performed a statistical analysis by using the neural network from HOLISMOKES IX to model these systems as singular isothermal ellipsoids with external shear and to estimate their parameter values, making this the largest uniformly modeled sample to date. We find a tendency towards larger Einstein radii for galaxy-scale systems in overdense environments, while the other parameter values as well as the uncertainty distributions are consistent between those in overdense and non-overdense environments. These results demonstrate the feasibility of downloading and applying neural network classifiers to hundreds of million cutouts, which will be needed in the upcoming era of big data from deep, wide-field imaging surveys such as Euclid and the Rubin Observatory Legacy Survey of Space and Time. At the same time, it offers a sample size that can be visually inspected by humans. These deep learning pipelines, with false-positive rates of $ are very powerful tools to identify such rare galaxy-scale strong lensing systems, while also aiding in the discovery of new strong lensing clusters.