HerMES: deep number counts at 250 μm, 350 μm and 500 μm in the COSMOS and GOODS-N fields and the build-up of the cosmic infrared background

Aims. The Spectral and Photometric Imaging REceiver (SPIRE) onboard the Herschel space telescope has provided confusion limited maps of deep fields at 250 mu m, 350 mu m, and 500 mu m, as part of the Herschel Multi-tiered Extragalactic Survey (HerMES). Unfortunately, due to confusion, only a small fraction of the cosmic infrared background (CIB) can be resolved into individually-detected sources. Our goal is to produce deep galaxy number counts and redshift distributions below the confusion limit at SPIRE wavelengths (similar to 20 mJy), which we then use to place strong constraints on the origins of the cosmic infrared background and on models of galaxy evolution. Methods. We individually extracted the bright SPIRE sources (>20 mJy) in the COSMOS field with a method using the positions, the flux densities, and the redshifts of the 24 mu m sources as a prior, and derived the number counts and redshift distributions of the bright SPIRE sources. For fainter SPIRE sources (<20 mJy), we reconstructed the number counts and the redshift distribution below the confusion limit using the deep 24 mu m catalogs associated with photometric redshift and information provided by the stacking of these sources into the deep SPIRE maps of the GOODS-N and COSMOS fields. Finally, by integrating all these counts, we studied the contribution of the galaxies to the CIB as a function of their flux density and redshift. Results. Through stacking, we managed to reconstruct the source counts per redshift slice down to similar to 2 mJy in the three SPIRE bands, which lies about a factor 10 below the 5s confusion limit. Our measurements place tight constraints on source population models. None of the pre-existing models are able to reproduce our results at better than 3-sigma. Finally, we extrapolate our counts to zero flux density in order to derive an estimate of the total contribution of galaxies to the CIB, finding 10.1 (+2.6)(2.3) nW m(-2) sr(-1), 6.5 (+1.7)(1.6) nW m(-2) sr(-1), and 2.8 (+0.9)(0.8) nW m(-2) sr(-1) at 250 mu m, 350 mu m, and 500 mu m, respectively. These values agree well with FIRAS absolute measurements, suggesting our number counts and their extrapolation are sufficient to explain the CIB. We find that half of the CIB is emitted at z = 1.04, 1.20, and 1.25, respectively. Finally, combining our results with other works, we estimate the energy budget contained in the CIB between 8 mu m and 1000 mu m: 26(-3)(+7) nW m(-2) sr(-1).