A halo model approach for mock catalogs of time-variable strong gravitational lenses

Time delays in both galaxy- and cluster-scale strong gravitational lenses have recently attracted a lot of attention in the context of the Hubble tension. Future wide-field cadenced surveys, such as the LSST, are anticipated to discover strong lenses across various scales. We generate mock catalogs of strongly lensed QSOs and SNe on galaxy-, group-, and cluster-scales based on a halo model that incorporates dark matter halos, galaxies, and subhalos. For the upcoming LSST survey, we predict that approximately 3500 lensed QSOs and 200 lensed SNe with resolved multiple images will be discovered. Among these, about 80 lensed QSOs and 10 lensed SNe will have maximum image separations larger than 10 arcsec, which roughly correspond to cluster-scale strong lensing. We find that adopting the Chabrier stellar IMF instead of the fiducial Salpeter IMF reduces the predicted number of strong lenses approximately by half, while the distributions of lens and source redshifts and image separations are not significantly changed. In addition to mock catalogs of multiple-image lens systems, we create mock catalogs of highly magnified systems, including both multiple-image and single-image systems. We find that such highly magnified systems are typically produced by massive galaxies, but non-negligible fraction of them are located in the outskirt of galaxy groups and clusters. Furthermore, we compare subsamples of our mock catalogs with lensed QSO samples constructed from the SDSS and Gaia to find that our mock catalogs with the fiducial Salpeter IMF reproduce the observation quite well. In contrast, our mock catalogs with the Chabrier IMF predict a significantly smaller number of lensed QSOs compared with observations, which adds evidence that the stellar IMF of massive galaxies is Salpeter-like. Our python code SL-Hammocks as well as the mock catalogs are made available online. (abridged)