Halo Properties and Mass Functions of Groups/Clusters from the DESI Legacy Imaging Surveys DR9

Based on a large group/cluster catalog recently constructed from the DESI Legacy Imaging Surveys DR9 using an extended halo-based group finder, we measure and model the group-galaxy weak-lensing signals for groups/clusters in a few redshift bins within redshift range 0.1 <= z < 0.6. Here, the background shear signals are obtained based on the DECaLS survey shape catalog, derived with the Fourier_Quad method. We divide the lens samples into five equispaced redshift bins and seven mass bins, which allow us to probe the redshift and mass dependence of the lensing signals, and hence the resulting halo properties. In addition to these sample selections, we also check the signals around different group centers, e.g., the brightest central galaxy, the luminosity-weighted center, and the number-weighted center. We use a lensing model that includes off-centering to describe the lensing signals that we measure for all mass and redshift bins. The results demonstrate that our model predictions for the halo masses, biases, and concentrations are stable and self-consistent among different samples for different group centers. Taking advantage of the very large and complete sample of groups/clusters, as well as the reliable estimations of their halo masses, we provide measurements of the cumulative halo mass functions up to redshift z = 0.6, with a mass precision at 0.03 similar to 0.09 dex.