The conditions under which galactic nuclear regions become active are largely unknown, although it has been hypothesized that secular processes related to galaxy morphology could play a significant role. We investigate this question using optical i-band images of 3096 SDSS quasars and galaxies at 0.3 < z < 0.6 from the Hyper Suprime-Cam Subaru Strategic Program, which possesses a unique combination of area, depth, and resolution, allowing the use of residual images, after removal of the quasar and smooth galaxy model, to investigate internal structural features. We employ a variational auto-encoder, which is a generative model that acts as a form of dimensionality reduction. We analyze the lower-dimensional latent space in search of features that correlate with nuclear activity. We find that the latent space does separate images based on the presence of nuclear activity, which appears to be associated with more pronounced components (i.e., arcs, rings, and bars) as compared to a matched control sample of inactive galaxies. These results suggest the importance of secular processes and possibly mergers (by their remnant features) in activating or sustaining black hole growth. Our study highlights the breadth of information available in ground-based imaging taken under optimal seeing conditions and having an accurate characterization of the point-spread function (PSF), thus demonstrating future science to come from the Rubin Observatory.
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