Herschel deep far-infrared counts through the Abell 2218 cluster-lens
  Gravitational lensing by massive galaxy clusters allows study of the
population of intrinsically faint infrared galaxies that lie below the
sensitivity and confusion limits of current infrared and submillimeter
telescopes. We present ultra-deep PACS 100 and 160 microns observations toward
the cluster lens Abell 2218, to penetrate the Herschel confusion limit. We
derive source counts down to a flux density of 1 mJy at 100 microns and 2 mJy
at 160 microns, aided by strong gravitational lensing. At these levels, source
densities are 20 and 10 beams/source in the two bands, approaching source
density confusion at 160 microns. The slope of the counts below the turnover of
the Euclidean-normalized differential curve is constrained in both bands and is
consistent with most of the recent backwards evolutionary models. By
integrating number counts over the flux range accessed by Abell 2218 lensing
(0.94-35 mJy at 100 microns and 1.47-35 mJy at 160 microns, we retrieve a
cosmic infrared background (CIB) surface brightness of ~8.0 and ~9.9 nW m^-2
sr^-1, in the respective bands. These values correspond to 55% (+/- 24%) and
77% (+/- 31%) of DIRBE direct measurements. Combining Abell 2218 results with
wider/shallower fields, these figures increase to 62% (+/- 25%) and 88% (+/-
32%) CIB total fractions, resolved at 100 and 160 microns, disregarding the
high uncertainties of DIRBE absolute values.
