How many galaxies fit in a halo? Constraints on galaxy formation efficiency from spatial clustering

We study galaxy clustering in the framework of halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, dark matter clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining nonlinear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles of the halo they inhabit, and galaxy formation efficiency is characterized by the number of galaxies that populate a halo of given 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. Both are in qualitatively agreement with measurements in galaxy catalogs. We find that requiring the model to fit both the second- and third-order moments of the Automatic Plate Measuring Facility (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 ≈ 10¹⁰ M_⊙ h^-1, whereas data at smaller scales require that the number of galaxies in a halo scale approximately 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 in this framework. Although halo models agree well with measurements of the mass power spectrum and the higher order S_p 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.