Confusion noise at far-IR to millimeter wavelengths

We present detailed predictions for the confusion noise due to extragalactic sources in the far-IR/(sub)-millimeter channels of ESA/ISO, NASA/Spitzer, ESA/Herschel and ESA/Planck satellites, including the contribution from clustering of unresolved SCUBA galaxies. Clustering is found to increase the confusion noise, compared to the case of purely Poisson fluctuations, by 10-15% for the lowest frequency (i.e. lowest angular resolution) Spitzer and Herschel channels, by 25-35% for the 175 micron ISOPHOT channel, and to dominate in the case of Planck/HFI channels at nu>143GHz. Although our calculations make use of a specific evolutionary model (Granato et al. 2004), 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 micron sources fainter than 2 mJy, consistent with the results by Peacock et al. (2000). This normalization yields, for the first model, r_0=8.3$ Mpc/h, and, for the second model, an effective mass of dark matter haloes in which these sources reside of M_halo=1.8*10^{13} M_sun/h. These results are consistent with independent estimates for SCUBA galaxies and for other, likely related, sources.