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In this paper, we investigate the physical associations between blendedfar-infrared (FIR)-emitting galaxies, in order to identify the level ofline-of-sight projection contamination in the single-dish Herschel data.Building on previous work, and as part of the Herschel Extragalactic LegacyProject (HELP), we identify a sample of galaxies in the COSMOS field which arefound to be both FIR-bright (typically $\sim 15$ mJy) and blended within theHerschel 250 $\mu$m beam. We identify a spectroscopic or photometric redshiftfor each FIR-bright source. We conduct a joint probability distributionanalysis on the redshift probability density functions to determine thefraction of the FIR sources with multiple FIR-bright counterparts which arelikely to be found at consistent ($\Delta z$ $< 0.01$) redshifts. We find thatonly 3 (0.4 per cent) of the pair permutations between counterparts are $>50$per cent likely to be at consistent redshifts. A majority of counterparts (72per cent) have no overlap in their redshift probability distributionswhatsoever. This is in good agreement with the results of recent simulations,which indicate that single-dish observations of the FIR sky should be stronglycontaminated by line of sight projection effects. We conclude that for oursample of 3.6- and 24-$\mu$m selected, FIR-bright objects in the COSMOS field,the overwhelming majority of multi-component FIR systems are line of sightprojections within the 18.1 arcsec Herschel beam, rather than physicalassociations.

Cosmic happenstance: 24-$\mu$m selected, multi-component Herschel sources are line-of-sight projections