Herschel-ATLAS/GAMA: SDSS cross-correlation induced by weak lensing

We report a highly significant ($>10\sigma$) spatial correlation between galaxies with $S_{350\mu\rm m}\ge 30\,$mJy detected in the equatorial fields of the \textsl{Herschel} Astrophysical Terahertz Large Area Survey (H-ATLAS) with estimated redshifts $\gtrsim 1.5$, and SDSS or GAMA galaxies at $0.2\le z\le 0.6$. The significance of the cross-correlation is much higher than those reported so far for samples with non-overlapping redshift distributions selected in other wavebands. Extensive, realistic simulations of clustered sub-mm galaxies amplified by foreground structures confirm that the cross-correlation is explained by weak gravitational lensing ($\mu<2$). The simulations also show that the measured amplitude and range of angular scales of the signal are larger than can be accounted for by galaxy-galaxy weak lensing. However, for scales $\lesssim 2\,$arcmin, the signal can be reproduced if SDSS/GAMA galaxies act as signposts of galaxy groups/clusters with halo masses in the range $10^{13.2}$--$10^{14.5} M_{\odot}$. The signal detected on larger scales appears to reflect the clustering of such halos.