Predicting sub-millimetre flux densities from global galaxy properties

Recent years have seen growing interest in post-processing cosmological simulations with radiative transfer codes to predict observable fluxes for simulated galaxies. However, this can be slow, and requires a number of assumptions in cases where simulations do not resolve the interstellar medium (ISM). Zoom-in simulations better resolve the detailed structure of the ISM and the geometry of stars and gas; ho wever, statistics are limited due to the computational cost of simulating even a single halo. In this paper, we make use of a set of high-resolution, cosmological zoom-in simulations of massive ( M-* sic 10(10.5) M-? at z = 2), star-forming galaxies from the FIRE suite. We run the SKIRT radiative transfer code on hundreds of snapshots in the redshift range 1.5 < z < 5 and calibrate a power-law scaling relation between dust mass, star formation rate, and 870 mu m flux density. The derived scaling relation shows encouraging consistency with observational results from the sub-millimetre-selected AS2UDS sample. We extend this to other wavelengths, deriving scaling relations between dust mass, stellar mass, star formation rate, and redshift and sub-millimetre flux density at observed-frame wavelengths between similar to 340 and similar to 870 mu m. We then apply the scaling relations to galaxies drawn from EAGLE, a large box cosmological simulation. We show that the scaling relations predict EAGLE sub-millimetre number counts that agree well with previous results that were derived using far more computationally expensiv e radiative transfer techniques. Our scaling relations can be applied to other simulations and semi-analytical or semi-empirical models to generate robust and fast predictions for sub-millimetre number counts.