Abstract
It is widely recognized that cold dark matter (CDM) models predict abundant dark matter substructure in halos of all sizes. Galaxy-galaxy lensing provides a unique opportunity to directly measure the presence and the mass of such substructures in clusters of galaxies. Here we present the mass function of substructures obtained from lensing in massive Hubble Space Telescope cluster lenses and compare it with that obtained from high-resolution cosmological N-body simulations. We find excellent agreement in the slope and amplitude in the mass range 1011-1012.5 M☉ probed by the observations, highlighting a significant success of the CDM theory. At lower mass scales, the simulations predict a large abundance of small substructures below our detection threshold with galaxy-galaxy lensing, with many of them being plausibly associated with faint cluster galaxies. Our results suggest that the CDM substructure abundance on the scale of clusters is in good agreement with present observational data.