HerMES: Candidate Gravitationally Lensed Galaxies and Lensing Statistics
  at Submillimeter Wavelengths
  We present a list of 13 candidate gravitationally lensed submillimeter
galaxies (SMGs) from 95 square degrees of the Herschel Multi-tiered
Extragalactic Survey, a surface density of 0.14\pm0.04deg^{-2}. The selected
sources have 500um flux densities (S_500) greater than 100mJy. Gravitational
lensing is confirmed by follow-up observations in 9 of the 13 systems (70%),
and the lensing status of the four remaining sources is undetermined. We also
present a supplementary sample of 29 (0.31\pm0.06deg^{-2}) gravitationally
lensed SMG candidates with S_500=80--100mJy, which are expected to contain a
higher fraction of interlopers than the primary candidates. The number counts
of the candidate lensed galaxies are consistent with a simple statistical model
of the lensing rate, which uses a foreground matter distribution, the intrinsic
SMG number counts, and an assumed SMG redshift distribution. The model predicts
that 32--74% of our S_500>100mJy candidates are strongly gravitationally lensed
(mu>2), with the brightest sources being the most robust; this is consistent
with the observational data. Our statistical model also predicts that, on
average, lensed galaxies with S_500=100mJy are magnified by factors of ~9, with
apparently brighter galaxies having progressively higher average magnification,
due to the shape of the intrinsic number counts. 65% of the sources are
expected to have intrinsic 500micron flux densities less than 30mJy. Thus,
samples of strongly gravitationally lensed SMGs, such as those presented here,
probe below the nominal Herschel detection limit at 500 micron. They are good
targets for the detailed study of the physical conditions in distant dusty,
star-forming galaxies, due to the lensing magnification, which can lead to
spatial resolutions of ~0.01" in the source plane.
