With the advent of wide-area submillimeter surveys , a large number of high-redshift gravitationally lensed dusty star-forming galaxies ( DSFGs ) has been revealed .
Due to the simplicity of the selection criteria for candidate lensed sources in such surveys , identified as those with S _ { 500 \mu m } > 100 mJy , uncertainties associated with the modelling of the selection function are expunged .
The combination of these attributes makes submillimeter surveys ideal for the study of strong lens statistics .
We carried out a pilot study of the lensing statistics of submillimetre-selected sources by making observations with the Atacama Large Millimetre Array ( ALMA ) of a sample of strongly-lensed sources selected from surveys carried out with the Herschel Space Observatory .
We attempted to reproduce the distribution of image separations for the lensed sources using a halo mass function taken from a numerical simulation which contains both dark matter and baryons .
We used three different density distributions , one based on analytical fits to the halos formed in the EAGLE simulation and two density distributions ( Singular Isothermal Sphere ( SIS ) and SISSA ) that have been used before in lensing studies .
We found that we could reproduce the observed distribution with all three density distributions , as long as we imposed an upper mass transition of \sim 10 ^ { 13 } M _ { \odot } for the SIS and SISSA models , above which we assumed that the density distribution could be represented by an NFW profile .
We show that we would need a sample of \sim 500 lensed sources to distinguish between the density distributions , which is practical given the predicted number of lensed sources in the Herschel surveys .