Weak-lensing halo numbers and dark-matter profiles

Integral measures of weak gravitational lensing by dark-matter haloes, like the aperture mass, are sensitive to different physical halo properties dep endent on the halo mass density profile. For isothermal profiles, the relat ion between aperture mass and virial mass is steeper than for haloes with t he universal NFW profile. Consequently, the halo mass range probed by the a perture mass is much wider for NFW than for isothermal haloes. We use recen t modifications to the Press-Schechter mass function in CDM models normalis ed to the local abundance of rich clusters, to predict the properties of th e halo sample expected to be accessible with the aperture mass technique. W hile similar to 10 haloes should be detected per square degree if the haloe s have NFW profiles, their number density is lower by approximately an orde r of magnitude if they have isothermal profiles. These results depend only very mildly on the cosmological background model. We conclude that counts o f haloes with a significant weak-lensing signal are a powerful discriminato r between different dark-matter profiles.