Clustering of galaxy clusters in cold dark matter universes

We use very large cosmological N -body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model ( τ CDM) and a flat low density model with a cosmological constant (ΛCDM). Our simulations each use 10⁹ particles to follow the mass distribution within cubes of side 2  h ⁻¹ Gpc ( τ CDM) and 3  h ⁻¹ Gpc (ΛCDM) with a force resolution better than 10⁻⁴ of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from     for samples with mean separation     to     for samples with     The lower value here corresponds to τ CDM and the upper to ΛCDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10 per cent using the simple model of Sheth, Mo & Tormen. This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the automated plate measurement (APM) cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for ΛCDM. The observed power spectrum (for a cluster sample of mean separation     ) lies significantly above the predictions of both models.     

An improved model for contraction of dark matter haloes in response to condensation of baryons

The cooling of gas in the centres of dark matter haloes is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. Following Gnedin et al., we improve this model by modifying the assumed invariant from M ( r ) r to     , where r and     are the current and orbit-averaged particle positions. We explore the effect of the bulge in the inner regions of the halo for different values of the bulge-to-disc mass ratio. We find that the bulge makes the velocity curve rise faster in the inner regions of the halo. We present an analytical fitting curve that describes the velocity curve of the halo after dissipation. The results should be useful for dark matter detection studies.     

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the Eulerian space distribution of the haloes, the model allows one to describe the evolution of the dark matter itself. It can also be used to describe density profiles, on scales larger than the virial radius of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.     

Constraints on a non-Gaussian cold dark matter model

We consider constraints on the structure formation model based on non-Gaussian fluctuations generated during inflation, which have     distributions. Using three data sets, the abundance of the clusters at z =0, moderate z and the correlation length, we show that constraints on the non-Gaussianity and the amplitude of fluctuations and the density parameter can be obtained. We obtain an upper bound for _m, and a lower bound for the non-Gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at z 0.6, for the spectrum parametrized by cold dark matter (CDM) shape parameter =0.23, we obtain an upper bound for the density parameter of _m0.5 and lower bounds for the amplitude of ₈0.7 and for the non-Gaussianity of fluctuations of G 2 ( m 200), where G =1 for Gaussian.     

Evolution of the mass function of dark matter haloes

We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, in a  50 h ⁻¹ Mpc  volume containing 80 million particles. Our low-redshift results allow us to probe low-σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the  10¹⁰–10¹¹ M_⊙  haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth & Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high-redshift  ( z ≃ 6) QSOs  , which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorithm.     

Neutrinos as cluster dark matter

The dynamical mass of clusters of galaxies, calculated in terms of MOdified Newtonian Dynamics (MOND), is a factor of 2 or 3 times smaller than the Newtonian dynamical mass but remains significantly larger than the observed baryonic mass in the form of hot gas and stars in galaxies. Here I consider further the suggestion that the undetected matter might be in the form of cosmological neutrinos with mass of the order of 2 eV. If the neutrinos and baryons have comparable velocity dispersions and if the two components maintain their cosmological density ratio, then the electron density in the cores of clusters should be proportional to T ^3/2, as appears to be true in non-cooling flow clusters. This is equivalent to the 'entropy floor' proposed to explain the steepness of the observed luminosity–temperature relation, but here preheating of the medium is not required. Two-fluid (neutrino–baryon) hydrostatic models of clusters, in the context of MOND, reproduce the observed luminosity–temperature relation of clusters. If the β law is imposed on the gas density distribution, then the self-consistent models predict the general form of the observed temperature profile in both cooling and non-cooling flow clusters.