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

We study galaxy clustering using halo models, where gravitational clusteringis described in terms of dark matter halos. At small scales, clusteringstatistics are dominated by halo density profiles, whereas at large scales,correlations are the result of combining non-linear perturbation theory withhalo biasing. Galaxies are assumed to follow the dark matter profiles, andgalaxy formation efficiency is given by the number of galaxies as a function ofhalo mass. This approach leads to generic predictions: the galaxy powerspectrum shows a power-law behavior even though the dark matter does not, andthe galaxy higher-order correlations show smaller amplitudes at small scalesthan their dark matter counterparts, as observed in galaxy catalogs. We findthat requiring to fit both the second and third order moments of the APMgalaxies provides a strong constraint on galaxy formation models. The data atlarge scales require that galaxy formation be relatively efficient at smallmasses, m =10^10 Msun/h, whereas data at smaller scales require that the numberof galaxies in a halo scale as the mass to the 0.8th power in the high-masslimit. These constraints are independent of those derived from the luminosityfunction or Tully-Fisher relation. We also predict the power spectrum,bispectrum, and higher-order moments of the mass density field. Although halomodels agree well with measurements of the mass power spectrum and the higherorder Sp parameters in N-body simulations, the model assumption that halos arespherical leads to disagreement in the configuration dependence of thebispectrum at small scales. We stress the importance of finite volume effectsin higher-order statistics and show how they can be estimated in this approach.Comment: 32 pages, 10 figures, submitted to ApJ. References adde