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 analyze cross-correlation spectra between the dark matter and different galaxy samples selected by luminosity, color or star formation rate. We compare the predictions to the recent detection by SDSS. We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 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 centers of the corresponding halos. We compute the redshift evolution of the cross-correlation amplitude and compare it to those of galaxies and dark matter. We also compute the galaxy-dark matter correlation coefficient and show it is close to unity on scales above r > 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.