ALMA observations of lensed Herschel sources : Testing the dark-matter halo paradigm

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.