Dust sub-millimetre emission in green valley galaxies

Context. Green valley (GV) galaxies are objects defined on a colour-magnitude diagram, or a colour-mass diagram, as being associated with a transition from a star-forming to a quiescent state (quenching), or vice versa (rejuvenation). Aims. We studied the sub-millimetre emission of galaxies in the GV and linked it with their physical evolutionary properties. Methods. We exploited a semi-analytic model (SAM) for galaxy evolution that includes a detailed treatment of dust production and evolution in galactic contexts. We modelled the observational properties of simulated galaxies by post-processing the SAM catalogues with the spectral synthesis and radiative transfer code GRASIL. Results. Our model produces a clear bimodality (and thus a GV) in the colour-mass diagram, although some tensions arise when compared to observations. After introducing a new criterion for identifying the GV in any dataset, we find that GV galaxies, at fixed stellar mass, have $250 \mu$m luminosities approximately half those of blue galaxies, while red galaxies exhibit luminosities of up to an order of magnitude lower. While specific star formation rates drop sharply during quenching, the dust content remains relatively high during the GV transition, powering sub-millimetre emission. Rejuvenating galaxies in the GV, which were previously red, have experienced a star formation burst that shifts their colour to green, but their $S_{250\, \mu \rm m}$ fluxes remain low due to their still low dust masses. Conclusions. Our galaxy evolution model highlights the delay between star formation and dust evolution, showing that sub-millimetre emission is not always a safe indicator of star formation activity, with quenching (rejuvenating) GV galaxies featuring relatively high (low) sub-millimetre emission.