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Jiun-Huei Proty Wu
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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.
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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.
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 $sigma_{sigma_8}=^{+0.120}_{-0.162}$.
By obtaining imaging data in two photometric bands for 60 lenticular galaxies - members of 8 southern clusters - with the Las Cumbres Observatory one-meter telescope network, we have analyzed the structure of their large-scale stellar disks. The parameters of radial surface-brightness profiles have been determined (including also disk thickness), and all the galaxies have been classified into pure exponential (Type I) disk surface-brightness profiles, truncated (Type II) and antitruncated (Type III) piecewise exponential disk surface-brightness profiles. We confirm the previous results of some other authors that the proportion of surface-brightness profile types is very different in environments of different density: in the clusters the Type-II profiles are almost absent while according to the literature data, in the field they constitute about one quarter of all lenticular galaxies. The Type-III profiles are equally presented in the clusters and in the field, while following similar scaling relations; but by undertaking an additional structural analysis including the disk thickness determination we note that some Type-III disks may be a combination of a rather thick exponential pseudobulge and an outer Type-I disk. Marginally we detect a shift of the scaling relation toward higher central surface brightnesses for the outer segments of Type-III disks and smaller thickness of the Type-I disks in the clusters. Both effects may be explained by enhanced radial stellar migration during disk galaxy infall into a cluster that in particular represents an additional channel for Type-I disk shaping in dense environments.
These lectures deal with our current knowledge of the matter distribution in the universe, focusing on how this is studied via the large-scale structure seen in galaxy surveys. We first assemble the necessary basics needed to understand the development of density fluctuations in an expanding universe, and discuss how galaxies are located within the dark-matter density field. Results from the 2dF Galaxy Redshift Survey are presented and contrasted with theoretical models. We show that the combination of large-scale structure and data on microwave-background anisotropies can eliminate almost all degeneracies, and yield a completely specified cosmological model. This is the concordance universe: a geometrically flat combination of vacuum energy and cold dark matter. The study of cosmic structure is able to establish this in a manner independent of external information, such as the Hubble diagram; this extra information can however be used to limit non-standard alternatives, such as a variable equation of state for the vacuum.
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