Constraints on Small-Scale Structures of Dark Matter from Flux Anomalies in Quasar Gravitational Lenses

Abstract

We address the question of whether the LambdaCDM model produces enough substructure in galaxy scale dark matter halos to cause the observed image flux anomalies in lensed QSOs observed in the radio and mid-infrared. We create a very large number of simulated lenses with finite source sizes to compare with the data. After analysing these simulations, our conclusions are: 1) The finite size of the source is important. The point source approximation commonly used can cause large and biased results. 2) When we randomly select lens models that are distorted from a Singular Isothermal Ellipsoid in reasonable ways, but do not contain substructure, the flux anomalies are not reproduced. 3) We find new upper bounds on the amount of substructure from the constraint that no simple single-galaxy lenses have been observed with a single source having more than four well separated images. 4) The lower bound on the amount of substructure is set by the frequency of image flux anomalies and is largely a bound on the surface mass density in substructure and not on the number density normalization and average mass separately. 5) Substructure models with the same size--mass relation produce similar numbers of flux anomalies even when their internal mass profiles are different. 6) Substructures with shallower mass profiles produce less extra images. 7) Assuming no constribution form extragalactic small-scale structure, we find a lower bound of ~ 0.3% on the fraction of mass in substructures within a projected distance of ~10 kpc from the center of a galaxy with velocity dispersion of 200 km/s. This bound is consistent with the results of LambdaCDM Nbody simulations.