How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering

We study galaxy clustering using halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining non-linear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles, and galaxy formation efficiency is given by the number of galaxies as a function of halo mass. This approach leads to generic predictions: the galaxy power spectrum shows a power-law behavior even though the dark matter does not, and the galaxy higher-order correlations show smaller amplitudes at small scales than their dark matter counterparts, as observed in galaxy catalogs. We find that requiring to fit both the second and third order moments of the APM galaxies provides a strong constraint on galaxy formation models. The data at large scales require that galaxy formation be relatively efficient at small masses, m =10^10 Msun/h, whereas data at smaller scales require that the number of galaxies in a halo scale as the mass to the 0.8th power in the high-mass limit. These constraints are independent of those derived from the luminosity function or Tully-Fisher relation. We also predict the power spectrum, bispectrum, and higher-order moments of the mass density field. Although halo models agree well with measurements of the mass power spectrum and the higher order Sp parameters in N-body simulations, the model assumption that halos are spherical leads to disagreement in the configuration dependence of the bispectrum at small scales. We stress the importance of finite volume effects in higher-order statistics and show how they can be estimated in this approach.