We present the recent merger history of massive galaxies in a spectroscopically confirmed proto-cluster at z = 1.62. Using Hubble Space Telescope WFC3 near-infrared imaging from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, we select cluster and z similar to 1.6 field galaxies with M-star >= 3 x 10(10) M-circle dot, to determine the frequency of double nuclei or close companions within projected separations less than 20 kpc co-moving. We find that four out of five spectroscopically confirmed massive proto-cluster galaxies have double nuclei, and 57(14)(+13)% of all Mstar >= 3 x 10(10) M-circle dot cluster candidates are observed in either close pair systems or have double nuclei. In contrast, only 11% +/- 3% of the field galaxies are observed in close pair/double nuclei systems. After correcting for the contribution from random projections, the implied merger rate per massive galaxy in the proto-cluster is similar to 3-10 times higher than the merger rate of massive field galaxies at z similar to 1.6. Close pairs in the cluster have minor merger stellar mass ratios (M-primary:M-satellite >= 4), while the field pairs consist of both major and minor mergers. At least half of the cluster mergers are gas-poor, as indicated by their red colors and low 24 mu m fluxes. Two of the double-nucleated cluster members have X-ray detected active galactic nuclei with L-x > 10(43) erg s(-1), and are strong candidates for dual or offset super-massive black holes. We conclude that the massive z = 1.62 proto-cluster galaxies are undergoing accelerated assembly via minor mergers, and discuss the implications for galaxy evolution in proto-cluster environments.
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