Understanding the halo-mass and galaxy-mass cross-correlation functions

We use the Millennium Simulation (MS) to measure the cross-correlation between halo centres and mass (or equivalently the average density profiles of dark haloes) in a Lambda cold dark matter (Lambda CDM) cosmology. We present results for radii in the range 10 h(-1) kpc < r < 30 h(-1) Mpc and for halo masses in the range 4 x 10(10) < M(200) < 4 x 10(14) h(-1) M(circle dot). Both at z = 0 and at z = 0.76 these cross-correlations are surprisingly well fitted if the inner region is approximated by a density profile of NFW or Einasto form, the outer region by a biased version of the linear mass autocorrelation function, and the maximum of the two is adopted where they are comparable. We use a simulation of galaxy formation within the MS to explore how these results are reflected in cross-correlations between galaxies and mass. These are directly observable through galaxy-galaxy lensing. Here also we find that simple models can represent the simulation results remarkably well, typically to less than or similar to 10 per cent. Such models can be used to extend our results to other redshifts, to cosmologies with other parameters, and to other assumptions about how galaxies populate dark haloes. Our galaxy formation simulation already reproduces current galaxy-galaxy lensing data quite well. The characteristic features predicted in the galaxy-galaxy lensing signal should provide a strong test of the Lambda CDM cosmology as well as a route to understanding how galaxies form within it.