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 Mpc/h), the galaxy bias is roughly linear and
deterministic. On smaller scales (R<5 Mpc/h) 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 Mpc/h), 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.
