Galaxy pairs with separations of only a few kpc represent important stages in the merger-driven growth of supermassive black holes (SMBHs). However, such mergers are difficult to identify observationally due to the correspondingly small angular scales. In Paper I we presented a method of finding candidate kpc-scale galaxy mergers that is leveraged on the selection of X-ray sources spatially offset from the centers of host galaxies. In this paper we analyze new Hubble Space Telescope (HST) WFC3 imaging for six of these sources to search for signatures of galaxy mergers. The HST imaging reveals that four of the six systems are on-going galaxy mergers with separations of 1.2-6.6 kpc (offset AGN). The nature of the remaining two spatially offset X-ray sources is ambiguous and may be associated with super-Eddington accretion in X-ray binaries. The ability of this sample to probe small galaxy separations and minor mergers makes it uniquely suited for testing the role of galaxy mergers for AGN triggering. We find that galaxy mergers with only one AGN are predominantly minor mergers with mass ratios similar to the overall population of galaxy mergers. By comparison, galaxy mergers with two AGN are biased toward major mergers and larger nuclear gas masses. Finally, we find that the level of SMBH accretion increases toward smaller mass ratios (major mergers). This result suggests the mass ratio effects not only the frequency of AGN triggering but also the rate of SMBH growth in mergers.
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