The image separation distribution of strong lenses: Halo versus subhalo populations

We present a halo model prediction of the image separation distribution of strong lenses. Our model takes account of the subhalo population, which has been ignored in previous studies, as well as the conventional halo population. Halos and subhalos are linked to central and satellite galaxies by adopting an universal scaling relation between masses of (sub-)halos and luminosities of galaxies. Our model predicts that 10%-20% of lenses should be caused by the subhalo population. The fraction of lensing by satellite galaxies (subhalos) peaks at ~1'' and decreases rapidly with increasing image separations. We compute fractions of lenses which lie in groups and clusters, and find them to be ~14% and ~4%, respectively: Nearly half of such lenses are expected to be produced by satellite galaxies, rather than central parts of halos. We also study mass distributions of lensing halos and find that even at image separations of ~3'' the deviation of lens mass distributions from isothermal profiles is large: At or beyond ~3'' image separations are enhanced significantly by surrounding halos. Our model prediction agrees reasonably well with observed image separation distributions from galaxy to cluster scales.