Galaxy--dark matter correlations applied to galaxy--galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N-body simulations to make predictions for galaxy—dark matter correlations and apply them to galaxy—galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1 h−1 Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy—dark matter correlation coefficient and show that it is close to unity on scales above 1 h−1 Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy—dark matter correlations.