High-redshift submillimetre-bright galaxies identified by blank field surveys at millimetre and submillimetre wavelengths appear in the region of the IRAC colour-colour diagrams previously identified as the domain of luminous active galactic nuclei (AGNs). Our analysis using a set of empirical and theoretical dusty starburst spectral energy distribution (SED) models shows that power-law continuum sources associated with hot dust heated by young (<100 Myr old), extreme starbursts at z>2 also occupy the same general area as AGNs in the IRAC colour-colour plots. A detailed comparison of the IRAC colours and SEDs demonstrates that the two populations are distinct from each other, with submillimetre-bright galaxies having a systematically flatter IRAC spectrum (>1 mag bluer in the observed [4.5]-[8.0] colour). Only about 20% of the objects overlap in the colour-colour plots, and this low fraction suggests that submillimetre galaxies powered by a dust-obscured AGN are not common. The red IR colours of the submillimetre galaxies are distinct from those of the ubiquitous foreground IRAC sources, and we propose a set of IR colour selection criteria for identifying SMG counterparts that can be used even in the absence of radio or Spitzer MIPS 24 micron data.
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