Statistical cluster-QSO weak lensing in the Sloan Digital Sky Survey

We investigate the cross-correlation between galaxy clusters and QSOs using Sloan Digital Sky Survey (SDSS) DR4 similar to 5000 deg(2) data. With photometric redshifts of galaxies, we select galaxy clusters based on the local projected densities of LRGs brighter than M-r' = -22. The QSOs are from the main sample of SDSS QSO spectroscopic survey to i' = 19. A significant positive correlation is found between the clusters and QSOs. Under the assumption that the signal is caused by gravitational lensing, we fit the signal with singular isothermal sphere (SIS) model and NFW profile halo model. The velocity dispersion sigma(v) = 766 km s(-1) is derived for the best-fit of SIS model. Best-fit for the NFW model requires the dark matter halo mass within 1.5 h(-1) Mpc to be 4.6 x 10(14) h(-1) M-.. The mass parameter Omega(cl) of the cluster sample is deduced as 0.077 with the SIS model and 0.083 with the NFW model. Our results of Omega(cl) are smaller than those given by Croom & Shanks and by Myers et al.