Confusion noise at far-infrared to millimetre wavelengths

We present detailed predictions for the confusion noise due to extragalactic sources in the far-infrared/(sub)millimetre channels of the ESA/SO, NASA/Spitzer, ESA/Herschel and ESA/Planck satellites, including the contribution from clustering of unresolved SCUBA galaxies. Compared to the case of purely Poisson fluctuations, clustering is found to increase the confusion noise by 10-15 per cent for the lowest frequency (i.e. lowest angular resolution) Spitzer and Herschel channels, and by 25-35 per cent for the 175-mum ISOPHOT channel, and to dominate in the case of Planck/HFI channels at nu greater than or equal to 143 GHz. Although our calculations make use of our recent specific evolutionary model, the results are strongly constrained by the observed counts and by data on the redshift distribution of SCUBA sources, and therefore are not expected to be heavily model-dependent. The main uncertainty arises from the poor observational definition of the source clustering properties. Two models have been used for the latter: a power law with constant slope and a redshift-independent comoving correlation length r(0); and the standard theoretical model for clustering evolution in a LambdaCDM universe, with a redshift-dependent bias factor. In both cases, the clustering amplitude has been normalized to yield a unit angular correlation function at theta(0) = 1 -2 arcsec for 850-mum sources fainter than 2 mJy, consistent with earlier results by Peacock et al. This normalization yields, for the first model, r(0) similar to 8.3 Mpc h(-1), and, for the second model, an effective mass of dark matter haloes in which these sources reside of M-halo similar to 1.8 x 10(13) M. h(-1). These results are consistent with independent estimates for SCUBA galaxies and for other, probably related, sources.