ALMACAL. XI. Over-densities as signposts to proto-clusters? A cautionary tale

It may be unsurprising that the most common approach to finding proto-clusters is to search for over-densities of galaxies. Upgrades to submillimetre (submm) interferometers and the advent of the James Webb Space Telescope will soon offer the opportunity to find more distant candidate proto-clusters in deep sky surveys without any spectroscopic confirmation. In this letter, we report the serendipitous discovery of an extremely dense region centred on the blazar, J0217-0820, at z=0.6 in the ALMACAL sky survey. Its density is eight times higher than that predicted by blind submm surveys. Among the seven submm-bright galaxies, three are as bright as conventional single-dish submm galaxies, with S_870um > 3mJy. The over-density is thus comparable to the densest known and confirmed proto-cluster cores. However, their spectra betray a wide range of redshifts. We investigate the likelihood of line-of-sight projection effects using light cones from cosmological simulations, finding that the deeper we search, the higher the chance that we will suffer from such projection effects. The extreme over-density around J0217-0820 demonstrates the strong cosmic variance we may encounter in the deep submm surveys. Thus, we should also question the fidelity of galaxy proto-cluster candidates selected via over-densities of galaxies, where the negative K correction eases the detection of dusty galaxies along an extraordinarily extended line of sight.