Angular Cross-Correlation of Galaxies: A Probe of Gravitational Lensing by Large-Scale Structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise due to spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line-of-sight. The lensing contribution to the 2-point auto-correlation function is typically small compared to the gravitational clustering. However the cross-correlation between two galaxy samples is nearly unaffected by gravitational clustering provided their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias due to lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of $\simeq 0.3$ and 1, we find a cross-correlation signal of $\simeq 1$ on arcminute scales and $\simeq 3$ on a few arcseconds. The dependence on the cosmological parameters $\mathrm{\Omega }$ and $\mathrm{\Lambda }$, on the dark matter power spectrum and on the bias factor of the foreground galaxy population is explored.