Constraints on the inner density profile of dark-matter haloes from weak gravitational lensing

We construct two linear filtering techniques based on weak gravitational lensing to constrain the inner slope $\alpha$ of the density profile of dark-matter halos. Both methods combine all available information into an estimate of this single number. Under idealised assumptions, $\alpha$ is constrained to ~15% if the halo concentration c is known, and to < 30% if not. We argue that the inevitable degeneracy between density-profile slope and halo concentration cannot be lifted under realistic conditions, and show by means of Fisher-matrix methods which linear combination of $\alpha$ and c is best constrained by our filtering of lensing data. This defines a new parameter, called P1, which is then constrained to ~15% for a single massive halo. If the signals of many halos can be stacked, their density profiles should thus be well constrained by the linear filters proposed here with the advantagebe insensitive to the cluster substructures.