HerMES: Deep Galaxy Number Counts from a P(D) Fluctuation Analysis of
  SPIRE Science Demonstration Phase Observations
  Dusty, star forming galaxies contribute to a bright, currently unresolved
cosmic far-infrared background. Deep Herschel-SPIRE images designed to detect
and characterize the galaxies that comprise this background are highly
confused, such that the bulk lies below the classical confusion limit. We
analyze three fields from the HerMES programme in all three SPIRE bands (250,
350, and 500 microns); parameterized galaxy number count models are derived to
a depth of ~2 mJy/beam, approximately 4 times the depth of previous analyses at
these wavelengths, using a P(D) (probability of deflection) approach for
comparison to theoretical number count models. Our fits account for 64, 60, and
43 per cent of the far-infrared background in the three bands. The number
counts are consistent with those based on individually detected SPIRE sources,
but generally inconsistent with most galaxy number counts models, which
generically overpredict the number of bright galaxies and are not as steep as
the P(D)-derived number counts. Clear evidence is found for a break in the
slope of the differential number counts at low flux densities. Systematic
effects in the P(D) analysis are explored. We find that the effects of
clustering have a small impact on the data, and the largest identified
systematic error arises from uncertainties in the SPIRE beam.
