The multiplicity of 250-$\mu$m Herschel sources in the COSMOS field
  We investigate the multiplicity of extragalactic sources detected by the
Herschel Space Observatory in the COSMOS field. Using 3.6- and 24-$\mu$m
catalogues, in conjunction with 250-$\mu$m data from Herschel, we seek to
determine if a significant fraction of Herschel sources are composed of
multiple components emitting at 250 $\mu$m. We use the XID+ code, using
Bayesian inference methods to produce probability distributions of the possible
contributions to the observed 250-$\mu$m flux for each potential component. The
fraction of Herschel flux assigned to the brightest component is highest for
sources with total 250-$\mu$m fluxes < 45 mJy; however, the flux in the
brightest component is still highest in the brightest Herschel sources. The
faintest 250-$\mu$m sources (30-45 mJy) have the majority of their flux
assigned to a single bright component; the second brightest component is
typically significantly weaker, and contains the remainder of the 250-$\mu$m
source flux. At the highest 250-$\mu$m fluxes (45-110 mJy), the brightest and
second brightest components are assigned roughly equal fluxes, and together are
insufficient to reach 100 per cent of the 250-$\mu$m source flux. This
indicates that additional components are required, beyond the brightest two
components, to reproduce the observed flux. 95 per cent of the sources in our
sample have a second component that contains more than 10 per cent of the total
source flux. Particularly for the brightest Herschel sources, assigning the
total flux to a single source may overestimate the flux contributed by around
150 per cent.
