The spherical infall model in a cosmological background density field

We discuss the influence of the cosmological background density field on the spherical infall model. The spherical infall model has been used in the PressSchechter formalism to evaluate the number abundance of clusters of galaxies, as well as to determine the density parameter of the Universe from the infalling flow. Therefore, the understanding of collapse dynamics plays a key role for extracting cosmological information. Here, we consider a modified version of the spherical infall model. We derive the mean field equations from the Newtonian fluid equations, in which the influence of cosmological background inhomogeneity is incorporated into the averaged quantities as the backreaction . By calculating the averaged quantities explicitly, we obtain simple expressions and find that, in the case of a scale-free power spectrum, density fluctuations with a negative spectral index make the infalling velocities slow. This suggests that we underestimate the density parameter when using the simple spherical infall model. In cases with the index n >0, the effect of background inhomogeneity could be negligible and the spherical infall model becomes a good approximation for infalling flows. We also present a realistic example with a cold dark matter power spectrum. In this case, the mean infall tends to be slow owing to the anisotropic random velocity.     

Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in the light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes, which provide a good fit to large numerical simulations; (3) more accurate mass–temperature relations from larger catalogues of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multiparameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on σ ₈, the normalization of the matter power spectrum on scales of 8  h ⁻¹ Mpc, as a function of the matter density and cosmological constant in a universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the normalization, approximately independent of power spectrum shape, can be expressed as constraints on σ at an appropriate cluster normalization scale R _Cl. We provide fitting formulas for R _Cl and σ ( R _Cl) for general cosmologies, as well as for σ ₈ as a function of cosmology and shape parameter Γ. For flat models we find approximately σ ₈≃(0.495_−0.037^+0.034)Ω_M^−0.60 for Γ=0.23, where the error bar is dominated by uncertainty in the mass–temperature relation.     

Constraints on cosmological and biasing models using active galactic nucleus clustering

We attempt to put constraints on different cosmological and biasing models by combining the recent clustering results of X-ray sources in the local ( z ≤0.1) and distant Universe ( z ∼1) . To this end we compare the measured angular correlation function for bright (Akylas et al.) and faint (Vikhlinin & Forman) ROSAT X-ray sources respectively with those expected in three spatially flat cosmological models. Taking into account the different functional forms of the bias evolution, we find that there are two cosmological models which match the data well. In particular, low-Ω_○ cosmological models (Ω_Λ=1−Ω_○=0.7) that contain either (i) high σ ₈^mass=1.13 value with galaxy merging bias, b ( z )∝(1+ z )^1.8 or (ii) low σ ₈^mass=0.9 with non-bias, b ( z ) ≡ 1 best reproduce the AGN clustering results, while τ CDM models with different bias behaviour are ruled out at a high significance level.     

The limits of bound structures in the accelerating Universe

According to the latest evidence, the Universe is entering an era of exponential expansion, where gravitationally bound structures will get disconnected from each other, forming isolated 'island universes'. In this scenario, we present a theoretical criterion to determine the boundaries of gravitationally bound structures and a physically motivated definition of superclusters as the largest bound structures in the Universe. We use the spherical collapse model self-consistently to obtain an analytical condition for the mean density enclosed by the last bound shell of the structure (2.36 times the critical density in the present Universe, assumed to be flat, with 30 per cent matter and 70 per cent cosmological constant, in agreement with the previous, numerical result of Chiueh & He). N -body simulations extended to the future show that this criterion, applied at the present cosmological epoch, defines a sphere that encloses ≈99.7 per cent of the particles that will remain bound to the structure at least until the scale parameter of the Universe is 100 times its present value. On the other hand, (28 ± 13) per cent of the enclosed particles are in fact not bound, so the enclosed mass overestimates the bound mass, in contrast with the previous, less rigorous criterion of, e.g. Busha and collaborators, which gave a more precise mass estimate. We also verify that the spherical collapse model estimate for the radial infall velocity of a shell enclosing a given mean density gives an accurate prediction for the velocity profile of infalling particles, down to very near the centre of the virialized core.     

Predicting the clustering of X-ray selected galaxy clusters in flux-limited surveys

We present a model to predict the clustering properties of X-ray selected clusters in flux-limited surveys. Our technique correctly accounts for past light-cone effects on the observed clustering and follows the non-linear evolution in redshift of the underlying dark matter correlation function and cluster bias factor. The conversion of the limiting flux of a survey into the corresponding minimum mass of the hosting dark matter haloes is obtained by using theoretical and empirical relations between mass, temperature and X-ray luminosity of galaxy clusters. Finally, our model is calibrated to reproduce the observed cluster counts adopting a temperature–luminosity relation moderately evolving with redshift. We apply our technique to three existing catalogues: the ROSAT Brightest Cluster Sample (BCS); the X-ray Brightest Abell-type Cluster sample (XBACs); and the ROSAT –ESO Flux-Limited X-ray sample (REFLEX). Moreover, we consider an example of possible future space missions with fainter limiting flux. In general, we find that the amplitude of the spatial correlation function is a decreasing function of the limiting flux and that the Einstein–de Sitter models always give smaller correlation amplitudes than open or flat models with low matter density parameter Ω_0m. In the case of the XBACs catalogue, the comparison with previous estimates of the observational spatial correlation shows that only the predictions of models with Ω_0m=0.3 are in good agreement with the data, while the Einstein–de Sitter models have too low a correlation strength. Finally, we use our technique to discuss the best strategy for future surveys. Our results show that, to study the clustering properties of X-ray selected clusters, the choice of a wide area catalogue, even with a brighter limiting flux, is preferable to a deeper, but smaller area, survey.     

The origin of spatial intermittency in the galaxy distribution

The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrödinger equation coupled to a Poisson equation determining the gravitational potential. This approach has a number of interesting features, many of which were pointed out in a seminal paper by Widrow & Kaiser. In particular we show that this approach yields an elegant reformulation of an idea of Jones concerning the origin of lognormal intermittency in the galaxy distribution.     

Large-scale bias in the Universe — II. Redshift-space bispectrum

The determination of the density parameter Ω₀ from the large-scale distribution of galaxies is one of the major goals of modern cosmology. However, if galaxies are biased tracers of the underlying mass distribution, linear perturbation theory leads to a degeneracy between Ω₀ and the linear bias parameter b , and the density parameter cannot be estimated. In Matarrese, Verde &38; Heavens we developed a method based on second-order perturbation theory to use the bispectrum to lift this degeneracy by measuring the bias parameter in an Ω₀-independent way. The formalism was developed assuming that one has perfect information on the positions of galaxies in three dimensions. In galaxy redshift surveys, the three-dimensional information is imperfect, because of the contaminating effects of peculiar velocities, and the resulting clustering pattern in redshift space is distorted. In this paper we combine second-order perturbation theory with a model for collapsed, virialized structures, to extend the method to redshift space, and demonstrate that the method should be successful in determining with reasonable accuracy the bias parameter from state-of-the-art surveys such as the Anglo-Australian 2 degree Field Survey and the Sloan Digital Sky Survey.     

Simulations of deep pencil-beam redshift surveys

We create mock pencil-beam redshift surveys from very large cosmological N -body simulations of two cold dark matter (CDM) cosmogonies, an Einstein–de Sitter model ( τ CDM) and a flat model with Ω₀=0.3 and a cosmological constant (ΛCDM). We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al. Simulation particles are tagged as 'galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our τ CDM (ΛCDM) simulation. A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum, without any apparent large-scale periodicity in the original redshift histogram. Although the simulated redshift histograms frequently display regularly spaced clumps, the spacing of these clumps varies between catalogues and there is no 'preferred' period over our many realizations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a τ CDM (ΛCDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced clumps with a significance as high as that of the real data. We conclude that in CDM universes, the regularity on a scale of ∼130  h ⁻¹ Mpc observed by Broadhurst et al. has a priori probability well below 10⁻³.     

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at z  ≃ 1.5 which have apparent stellar ages of ≳ 3 Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations: damped Lyα absorbers and Lyman-limit galaxies at z  ≃ 3.2. If the collapse redshifts for the old red galaxies are in the range z _c ≃ 6–8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately ν ≃ 3.0 fluctuations, implying a very large bias parameter b  ≃ 6. If the collapse redshifts of the red galaxies are indeed in the range z _c = 6–8 required for power spectrum consistency, their implied ages at z  ≃ 1.5 are between 3 and 3.8 Gyr for essentially any model universe of current age 14 Gyr. The age of these objects as deduced from gravitational collapse thus provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star formation rate measured at z  < 5; there is no evidence for a general era of spheroid formation at extreme redshifts.