This changes the clustering pattern in a non-trivial way and it is therefore important to include these effects when studying the relation between the galaxy and the dark-matter power spectrum.
Redshift-space distortions enhance the correlations on large-linear scales and suppress them on small scales. Previous work in the halo model has focused on the clustering in real space, while most of existing and upcoming surveys operate in redshift space. These features naturally explain many of the observational properties of galaxy clustering in real space, such as the power-law growth on small scales and the delayed onset of non-linear clustering in the translinear regime ( Peacock & Smith 2000 Seljak 2000 Scoccimarro et al. In addition to the multiplicity function there is another effect that changes the galaxy clustering properties: one galaxy is expected to form at the halo centre, which enhances the correlations on small scales. Above the threshold the number of galaxies increases with the halo mass, but need not grow linearly, as suggested by the gas cooling arguments, where gas in more massive and thus hotter haloes takes longer to cool and form stars. For a magnitude-limited sample this function is zero for low-mass haloes which cannot host bright L∗ galaxies, which already implies that galaxies cannot trace dark matter exactly. Galaxies differ from the dark matter in their galaxy multiplicity function, which parametrizes the number of galaxies inside the halo as a function of halo mass. This approach has been successful in reproducing the non-linear dark-matter power spectrum and its transition to the linear regime ( Ma & Fry 2000 Seljak 2000 Scoccimarro et al. For the latter, one needs to specify the radial halo profile, which can also be a function of halo mass.
To these correlations important on large scales one adds correlations on small scales, which arise from within the same haloes. These haloes cluster according to the linear theory, up to an overall amplitude which depends on the halo mass (halo biasing). In this model all the mass in the Universe is divided up into haloes of different masses. The relation between galaxies and dark-matter clustering has recently been analysed in the context of the halo model ( Peacock & Smith 2000 Seljak 2000 Scoccimarro et al. One of the purposes of this paper is to investigate how serious this problem is and, more generally, what is the relation between the observed redshift-space galaxy power spectrum and the underlying linear dark-matter spectrum. A possible concern is that the effect of massive neutrinos becomes important on small scales, where the assumption of galaxies tracing dark matter may not hold. In principle, the sensitivity of upcoming surveys is such that it will be possible to test neutrino masses below ( Hu, Eisenstein & Tegmark 1998), close to those suggested by recent Super-Kamiokande neutrino results ( Fukuda et al. Massive neutrinos have only a minor impact on the CMB, but they strongly suppress the level of mass fluctuations on small scales because of their high-neutrino momentum before they become non-relativistic. Mass power spectrum is particularly important for determination of the neutrino mass. This sensitivity is further improved if additional information from cosmic microwave background (CMB) anisotropies is included ( Eisenstein, Hu & Tegmark 1999). The three-dimensional mass power spectrum is sensitive to a number of cosmological parameters, such as the matter and baryon density, shape and amplitude of initial fluctuations and the Hubble constant. Upcoming surveys, such as Two Degree Field (2dF) 1 and Sloan Digital Sky Survey (SDSS) 2, will measure redshifts of up to a million galaxies. 2000), which has a near spherical geometry and consists of about 15 000 measured galaxy redshifts. Current state of the art is PSC z ( Saunders et al. Most problematic are galaxies predominantly found in groups and clusters, such as bright, red or elliptical galaxies, where we find poor convergence to a constant bias or β even on large scales.ĭetermination of the power spectrum of mass fluctuations is one of the main goals of existing and upcoming galaxy surveys. We show that linear bias is a good approximation only on large scales, for k0.1 h Mpc −1. We analyse scale dependence of redshift-space bias b and β ≡ Ω m 0.6/b in the context of the halo model.
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