Galaxy Morphologies Revealed with Subaru HSC and Super-Resolution Techniques II: Environmental Dependence of Galaxy Mergers at z 2-5

We super-resolve the seeing-limited Subaru Hyper Suprime-Cam (HSC) images for 32,187 galaxies at z 2-5 in three techniques, namely, the classical Richardson-Lucy (RL) point spread function (PSF) deconvolution, sparse modeling, and generative adversarial networks to investigate the environmental dependence of galaxy mergers. These three techniques generate overall similar high spatial resolution images but with some slight differences in galaxy structures, for example, more residual noises are seen in the classical RL PSF deconvolution. To alleviate disadvantages of each technique, we create combined images by averaging over the three types of super-resolution images, which result in galaxy sub-structures resembling those seen in the Hubble Space Telescope images. Using the combined super-resolution images, we measure the relative galaxy major merger fraction corrected for the chance projection effect, f_merg, for galaxies in the  300 deg^2-area data of the HSC Strategic Survey Program and the CFHT Large Area U-band Survey. Our f_merg measurements at z 3 validate previous findings showing that f_merg is higher in regions with a higher galaxy overdensity delta at z 2-3. Thanks to the large galaxy sample, we identify a nearly linear increase in f_merg with increasing delta at z 4-5, providing the highest-z observational evidence that galaxy mergers are related to delta. In addition to our f_merg measurements, we find that the galaxy merger fractions in the literature also broadly align with the linear f_merg-delta relation across a wide redshift range of z 2-5. This alignment suggests that the linear f_merg-delta relation can serve as a valuable tool for quantitatively estimating the contributions of galaxy mergers to various environmental dependences. This super-resolution analysis can be readily applied to datasets from wide field-of-view space telescopes such as Euclid and Roman.