Analytic model for galaxy and dark matter clustering

Abstract

We investigate an analytic model to compute the non-linear power spectrum of dark matter, galaxies and their cross-correlation. The model is based on Press-Schechter haloes, which cluster and have realistic dark matter profiles. The total power spectrum is a sum of two contributions, one from correlations between the haloes and one from correlations within the same halo. We show that such a model can give dark matter power spectra which match well with the results of N-body simulations, provided that the concentration parameter decreases with the halo mass. The galaxy power spectrum differs from the dark matter power spectrum because the pair-weighted number of galaxies does not scale with the halo mass and because most haloes harbour a central galaxy. If the pair-weighted number of galaxies increases less rapidly than the halo mass, as predicted by theoretical models and observed in clusters, then the resulting power spectrum becomes a power law with a slope close to the observed over several orders of magnitude in scale. Such a model also predicts a later onset of non-linear clustering in comparison with dark matter, which is needed to reconcile the cold dark matter (CDM) models with the data. A generic prediction of this model is that bias is scale-dependent and non-monotonic. This is particularly important for red or elliptical galaxies, which are preferentially found in larger mass haloes and for which the bias in the power spectrum may be scale-dependent even on large scales. Our predictions for galaxy-dark matter correlations, which can be observed through galaxy-galaxy lensing, show that these cannot be interpreted simply as an average halo profile of a typical galaxy, because different halo masses dominate at different scales and because larger haloes host more than one galaxy. We compute predictions for the cross-correlation coefficient as a function of scale and discuss the prospects of using cross-correlations in combination with galaxy clustering to determine the dark matter power spectrum.