The self-similarity of weak lensing peaks

We study the statistics of weak lensing convergence peaks, such as their abundance and two-point correlation function (2PCF), for a wide range of cosmological parameters Omega(m) and sigma(8) within the standard Lambda CDM paradigm, focusing on intermediate-height peaks with signal-to-noise ratio (SNR) of 1.5-3.5. We find that the cosmology dependence of the peak abundance can be described by a one-parameter fitting formula that is accurate to within similar to 3 per cent. The peak 2PCFs are shown to feature a self-similar behaviour: if the peak separation is rescaled by the mean interpeak distance, catalogues with different minimum peak SNR values have identical clustering, which suggests that the peak abundance and clustering are closely interconnected. A simple fitting model for the rescaled 2PCF is given, which together with the peak abundance model above can predict peak 2PCFs with an accuracy better than similar to 5 per cent. The abundance and 2PCFs for intermediate peaks have very different dependencies on Omega(m) and sigma(8), implying that their combination can be used to break the degeneracy between these two parameters.