We present strong empirical evidence for a physical connection between the occurrence of a starburst (SB) and a luminous AGN phase. Drawing infrared (IR), X-ray, and optically selected samples from COSMOS, we find that the locus of type-2 AGN hosts in the optical colour-magnitude (U-V/V) and colour-colour (U-V/V-J) space significantly overlaps with that of IR-luminous (L_IR > 10^10 L_sun) galaxies. Based on our observations, we propose that, when simultaneously building their black hole and stellar masses, type-2 AGN hosts are located in the same part of colour-colour space as dusty star-forming galaxies. In fact, our results show that IR-luminous galaxies at z<1.5 are on average 3 times more likely to host a type-2 AGN (L_X > 10^42 erg/s) than would be expected serendipitously, if AGN and star-formation events were unrelated. In addition, the optical and infrared properties of the AGN/SB hybrid systems tentatively suggest that the AGN phase might be coeval with a particularly active phase in a galaxy's star-formation history. Interestingly, we also find a significant fraction of type-2 AGN hosts offset from the dusty galaxy sequence in colour-colour space, possibly representing a transitional or post-starburst phase in galaxy evolution. Our findings are consistent with a scenario whereby AGN play a role in the termination of star-formation in massive galaxies.

9 pages, 8 figures, accepted for publication in MNRAS