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

Recent observational evidence suggests that the coarse angular resolution [similar to 20 arcsec full width at half maximum (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 deg(2) at 850 mu m, 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 (S-850 mu m greater than or similar to 1 mJy). Typically, three to six galaxies contribute 90 per cent of the flux of an S-850 mu m = 5 mJy source and these blended galaxies are physically unassociated. We find that field-to-field variations are comparable to Poisson fluctuations for our S-850 mu m > 5 mJy SMG population, which has a median redshift z(50) = 2.0, but are greater than Poisson for the S-850 mu m > 1 mJy population (z(50) = 2.8). In a detailed comparison to a recent interferometric survey targeted at single-dish detected sources, we reproduce the difference between single-dish and interferometer number counts and find a median redshift (z(50) = 2.5) in excellent agreement with the observed value (z(50) = 2.5 +/- 0.2). We also present predictions for single-dish survey number counts at 450 and 1100 mu m, which show good agreement with observational data.