Simulated observations of sub-millimetre galaxies: the impact of single-dish resolution and field variance

Recent observational evidence suggests that the coarse angular resolution ( ∼ 20′ ′ FWHM) of single-dish telescopes at sub-mm wavelengths has biased the observed galaxy number counts by blending together the sub-mm emission from multiple sub-mm galaxies (SMGs). We use lightcones computed from an updated implementation of the GALFORM semi-analytic model to generate 50 mock sub-mm surveys of 0.5 deg2 at 850 µm, taking into account the effects of the finite single-dish beam in a more accurate way than has been done previously. We find that blending of SMGs does lead to an enhancement of source extracted number counts at bright fluxes (S850µm & 1 mJy). Typically, ∼ 4 galaxies contribute 90 % of the flux of an S850µm = 5 mJy source and these blended galaxies are physically unassociated. We find that field-to-field variations are comparable to Poisson fluctuations for our S850µm> 5 mJy SMG population, which has a median redshift z50 = 2.05, but are greater than Poisson for the S850µm> 1 mJy population (z50 = 2.77). In a detailed comparison with the ALESS survey we reproduce the difference between single-dish and interferometer number counts, as well as the high-redshift tail of the observed photometric redshift distribution and find a median redshift (z50 = 2.58) consistent with the observed value (z50 = 2.5 ± 0.2). We also present predictions for single-dish survey number counts at 450 and 1100 µm which show good agreement with observational data. Key words: galaxies: sub-millimetr