Noise properties of gravitational lens mass reconstruction

Gravitational lensing is potentially able to observe mass-selected halos, and to measure the projected cluster mass function. An optimal mass-selection requires a quantitative understanding of the noise behavior in mass maps. This paper is an analysis of the noise properties in mass maps reconstructed using a maximum likelihood method. The noise power spectrum and the mass error bars are derived as a straightforward extension of the Kaiser & Squires (1993) algorithm to the case of a correlated noise. A very good agreement is found between these calculations and the noise properties observed in maximum likelihood mass reconstructions limited to simulated non-critical clusters of galaxies. In a second part, I show that the statistic of peaks in the noise follows accurately the peak statistics of a two-dimensional Gaussian random field (using the BBKS technics) if the smoothing aperture contains enough galaxies. This analysis provides a procedure to derive the significance of any mass peak as a function of its amplitude and its profile. It is demonstrated that, to a very good approximation, a mass map is the sum of the lensing signal plus a 2D gaussian random noise, which means that a detailled quantitative analysis of the structures in mass maps can be done. A direct application is the measurement of the projected mass function in wide field lensing surveys, down to small mass halos which are individually undetectable, this is the subject of a forthcoming work.