An exploration of galaxy-galaxy lensing and galaxy clustering in the Millennium-XXL simulation

The combination of galaxy-galaxy lensing and galaxy clustering data has the potential to simultaneously constrain both the cosmological and galaxy formation models. In this paper, we perform a comprehensive exploration of these signals and their covariances through a combination of analytic and numerical approaches. First, we derive analytic expressions for the projected galaxy correlation function and stacked tangential shear profile and their respective covariances, which include Gaussian and discreteness noise terms. Secondly, we measure these quantities from mock galaxy catalogues obtained from the Millennium-XXL simulation and semi-analytic models of galaxy formation. We find that on large scales (R > 10 h^-1 Mpc), the galaxy bias is roughly linear and deterministic. On smaller scales (R ≲ 5 h^-1 Mpc), the bias is a complicated function of scale and luminosity, determined by the different spatial distribution and abundance of satellite galaxies present when different magnitude cuts are applied, as well as by the mass dependence of the host haloes on magnitude. Our theoretical model for the covariances provides a reasonably good description of the measured ones on small and large scales. However, on intermediate scales (1 < R < 10 h^-1 Mpc), the predicted errors are ∼2-3 times smaller, suggesting that the inclusion of higher order, non-Gaussian terms in the covariance will be required for further improvements. Importantly, both our theoretical and numerical methods show that the galaxy-galaxy lensing and clustering signals have a non-zero cross-covariance matrix with significant bin-to-bin correlations. Future surveys aiming to combine these probes must take this into account in order to obtain unbiased and realistic constraints.