The correspondence between convergence peaks from weak lensing and massive dark matter haloes

The convergence peaks, constructed from galaxy shape measurement in weak lensing, are a powerful probe of cosmology as the peaks can be connected with the underlined dark matter haloes. However, the capability of convergence peak statistic is affected by the noise in galaxy shape measurement, signal-to-noise ratio (SNR), as well as the contribution from the projected mass distribution from the large-scale structures along the line of sight (LOS). In this paper, we use the ray-tracing simulation on a curved sky to investigate the correspondence between the convergence peak and the dark matter haloes at the LOS. We find that, in case of no noise and for source galaxies at z(s) = 1, more than 65 per cent peaks with SNR >= 3 (SNR) are related to more than one massive haloes with mass larger than 10(13)M(circle dot). Those massive haloes contribute 87.2 per cent to high peaks (SNR >= 5) and the remaining contributions are from the large-scale structures. On the other hand, the peak distribution is skewed by the noise in galaxy shape measurement, especially for lower SNR peaks. In the noisy field where the shape noise is modelled as a Gaussian distribution, about 60 per cent high peaks (SNR >= 5) are true peaks and the fraction decreases to 20 per cent for lower peaks (3 <= SNR < 5). Furthermore, we find that high peaks (SNR >= 5) are dominated by very massive haloes larger than 10(14) M-circle dot.