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Register a new userThe REFLEX Galaxy Cluster Survey VII: Omega_m and sigma_8 from cluster abundance and large-scale clustering
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For the first time the large-scale clustering and the mean abundance of galaxy clusters are analysed simultaneously to get precise constraints on the normalized cosmic matter density $Omega_m$ and the linear theory RMS fluctuations in mass $sigma_8$. A self-consistent likelihood analysis is described which combines, in a natural and optimal manner, a battery of sensitive cosmological tests where observational data are represented by the (Karhunen-Lo{e}ve) eigenvectors of the sample correlation matrix. This method breaks the degeneracy between $Omega_m$ and $sigma_8$. The cosmological tests are performed with the ROSAT ESO Flux-Limited X-ray (REFLEX) cluster sample. The computations assume cosmologically flat geometries and a non-evolving cluster population mainly over the redshift range $0<z<0.3$. The REFLEX sample gives the cosmological constraints and their $1sigma$ random errors of $Omega_m = 0.341 ^{+0.031}_{-0.029}$ and $sigma_8 = 0.711 ^{+0.039}_{-0.031}$. Possible systematic errors are evaluated by estimating the effects of uncertainties in the value of the Hubble constant, the baryon density, the spectral slope of the initial scalar fluctuations, the mass/X-ray luminosity relation and its intrinsic scatter, the biasing scheme, and the cluster mass density profile. All these contributions sum up to total systematic errors of $sigma_{Omega_m}=^{+0.087}_{-0.071}$ and $sigma_{sigma_8}=^{+0.120}_{-0.162}$.
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We show that the counts of galaxy clusters in future deep cluster surveys can place strong constraints on the matter density, Omega_m, the vacuum energy density, Omega_L, and the normalization of the matter power spectrum, sigma_8. Degeneracies between these parameters are different from those in studies of either high--redshift type Ia Supernovae (SNe), or cosmic microwave background (CMB) anisotropies. Using a mass threshold for cluster detection expected to be typical for upcoming SZE surveys, we find that constraints on Omega_m and sigma_8 at the level of roughly 5% or better can be expected, assuming redshift information is known at least to z=0.5 and in the absence of significant systematic errors. Without information past this redshift, Omega_L is constrained to 25%. With complete redshift information, deep (M_{lim}= 10^{14}h^{-1}{M_sun}), relatively small solid angle (roughly 12 {deg}^2) surveys can further constrain Omega_L to an accuracy of 15%, while large solid angle surveys with ground-based large-format bolometer arrays could measure Omega_L to a precision of 4% or better.
We use the presently observed number density of large X-ray clusters and linear mass power spectra to constrain the shape parameter ($Gamma$), the spectral index ($n$), the amplitude of matter density perturbations on the scale of $8 h^{-1}$Mpc ($sigma_8$), and the redshift distortion parameter ($beta$). The non-spherical-collapse model as an improvement to the Press-Schechter formula is used and yields significantly lower $sigma_8$ and $beta$. An analytical formalism for the formation redshift of halos is also derived.
We present the final data from the spectroscopic survey of the ROSAT-ESO Flux-Limited X-ray (REFLEX) catalog of galaxy clusters. The REFLEX survey covers 4.24 steradians (34% of the entire sky) below a declination of 2.5 deg and at high Galactic latitude (|b| > 20 deg). The REFLEX catalog includes 447 entries with a median redshift of 0.08 and is better than 90% complete to a limiting flux fx = 3x10^{-12} erg s^{-1} cm^{-2} (0.1 to 2.4 keV), representing the largest statistically homogeneous sample of clusters drawn from the ROSAT All-Sky Survey (RASS) to date. Here we describe the details of the spectroscopic observations carried out at the ESO 1.5 m, 2.2 m, and 3.6 m telescopes, as well as the data reduction and redshift measurement techniques. The spectra typically cover the wavelength range 3600-7500 A at a FWHM resolution of ~14 A, and the measured redshifts have a total rms error of ~100 km s^{-1}. In total we present 1406 new galaxy redshifts in 192 clusters, most of which previously did not have any redshift measured. Finally, the luminosity/redshift distributions of the cluster sample and a comparison to the no-evolution expectations from the cluster X-ray luminosity function are presented.
I review the status of large-scale structure studies based on redshift surveys of galaxies and clusters of galaxies. In particular, I compare recent results on the power spectrum and two-point correlation correlation function from the 2dF and REFLEX surveys, highlighting the advantage of X-ray clusters in the comparison to cosmological models, given their easy-to-understand mass selection function. Unlike for galaxies, this allows the overall normalization of the power spectrum to be measured directly from the data, providing an extra constraint on the models. In the context of CDM models, both the shape and amplitude of the REFLEX P(k) require, consistently, a low value for the mean matter density $Omega_M$. This shape is virtually indistinguishable from that of the galaxy power spectrum measured by the 2dF survey, simply multiplied by a constant cluster-galaxy bias factor. This consistency is remarkable for data sets which use different tracers and are very different in terms of selection function and observational biases. Similarly, the knowledge of the power spectrum normalization yields naturally a value $bsimeq 1$ for the bias parameter of $b_J$-selected (as in 2dF) galaxies, also in agreement with independent estimates using higher-order clustering and CMB data. In the final part, I briefly describe the measurements of the matter density parameter from redshift space distortions in galaxy surveys, and show evidence for similar streaming motions of clusters in the REFLEX redshift-space correlation function $xi(r_p,pi)$. With no exception, this wealth of independent clustering measurements point in a remarkably consistent way towards a low-density CDM Universe with $Omega_Msimeq 0.3$.
The origin of the micro-Gauss magnetic fields in galaxy clusters is one of the outstanding problem of modern cosmology. We have performed three-dimensional particle-in-cell simulations of the nonrelativistic Weibel instability in an electron-proton plasma, in conditions typical of cosmological shocks. These simulations indicate that cluster fields could have been produced by shocks propagating through the intergalactic medium during the formation of large-scale structure or by shocks within the cluster. The strengths of the shock-generated fields range from tens of nano-Gauss in the intercluster medium to a few micro-Gauss inside galaxy clusters.
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