Noise properties of gravitational lens mass reconstruction

Gravitational lensing is potentially able to observe mass‐selected haloes, and to measure the projected cluster mass function. An optimal mass selection requires a quantitative understanding of the noise behaviour in mass maps. This paper is an analysis of the noise properties in mass maps reconstructed from a maximum‐likelihood method. The first part of this work is the derivation of the noise power spectrum and the mass error bars as a straightforward extension of the Kaiser & Squires algorithm for the case of a correlated noise. Very good agreement is found between these calculations and the noise properties measured in the mass reconstructions limited to non‐critical clusters of galaxies. It demonstrates that Kaiser & Squires and maximum‐likelihood methods have similar noise properties and that the weak lensing approximation is valid for describing these properties. In a second stage I show that the statistics of peaks in the noise follows accurately the peak statistics of a two‐dimensional Gaussian random field (using the BBKS techniques) if the smoothing aperture contains enough galaxies. This analysis provides a full procedure for deriving the significance of any convergence peak as a function of its amplitude and profile. I demonstrate that a detailed quantitative analysis of the structures in mass maps can be carried out, and that, to a very good approximation, a mass map is the sum of the lensing signal and known two‐dimensional Gaussian random noise. A straightforward application is the measurement of the projected mass function in wide‐field lensing surveys, down to small mass overdensities that are individually undetectable.