81,956 research outputs found
The Correlation Function of Rich Clusters of Galaxies in CDM-like Models
We use ensembles of high-resolution CDM simulations to investigate the shape
and amplitude of the two point correlation function of rich clusters. The
standard scale-invariant CDM model with provides a poor description
of the clustering measured from the APM rich cluster redshift survey, which is
better fitted by models with more power at large scales. The amplitudes of the
rich cluster correlation functions measured from our models depend weakly on
cluster richness. Analytic calculations of the clustering of peaks in a
Gaussian density field overestimate the amplitude of the N-body cluster
correlation functions, but reproduce qualitatively the weak trend with cluster
richness. Our results suggest that the high amplitude measured for the
correlation function of richness class Abell clusters is either an
artefact arising from incompleteness in the Abell catalogue, or an indication
that the density perturbations in the early universe were very non-Gaussian.Comment: uuencoded compressed postscript ,MNRAS, in press, OUAST-93-1
Environmental Effects on Real-Space and Redshift-Space Galaxy Clustering
Galaxy formation inside dark matter halos, as well as the halo formation
itself, can be affected by large-scale environments. Evaluating the imprints of
environmental effects on galaxy clustering is crucial for precise cosmological
constraints with data from galaxy redshift surveys. We investigate such an
environmental impact on both real-space and redshift-space galaxy clustering
statistics using a semi-analytic model derived from the Millennium Simulation.
We compare clustering statistics from original SAM galaxy samples and shuffled
ones with environmental influence on galaxy properties eliminated. Among the
luminosity-threshold samples examined, the one with the lowest threshold
luminosity (~0.2L_*) is affected by environmental effects the most, which has a
~10% decrease in the real-space two-point correlation function (2PCF) after
shuffling. By decomposing the 2PCF into five different components based on the
source of pairs, we show that the change in the 2PCF can be explained by the
age and richness dependence of halo clustering. The 2PCFs in redshift space are
found to change in a similar manner after shuffling. If the environmental
effects are neglected, halo occupation distribution modeling of the real-space
and redshift-space clustering may have a less than 6.5% systematic uncertainty
in constraining beta from the most affected SAM sample and have substantially
smaller uncertainties from the other, more luminous samples. We argue that the
effect could be even smaller in reality. In the Appendix, we present a method
to decompose the 2PCF, which can be applied to measure the two-point
auto-correlation functions of galaxy sub-samples in a volume-limited galaxy
sample and their two-point cross-correlation functions in a single run
utilizing only one random catalog.Comment: 13 pages, 6 figures, Accepted by AP
Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions
We present an analytic model for the fully nonlinear power spectrum P and
bispectrum Q of the cosmological mass density field. The model is based on
physical properties of dark matter halos, with the three main model inputs
being analytic halo density profiles, halo mass functions, and halo-halo
spatial correlations, each of which has been well studied in the literature. We
demonstrate that this new model can reproduce the power spectrum and bispectrum
computed from cosmological simulations of both an n=-2 scale-free model and a
low-density cold dark matter model. To enhance the dynamic range of these large
simulations, we use the synthetic halo replacement technique of Ma & Fry
(2000a), where the original halos with numerically softened cores are replaced
by synthetic halos of realistic density profiles. At high wavenumbers, our
model predicts a slope for the nonlinear power spectrum different from the
often-used fitting formulas in the literature based on the stable clustering
assumption. Our model also predicts a three-point amplitude Q that is scale
dependent, in contrast to the popular hierarchical clustering assumption. This
model provides a rapid way to compute the mass power spectrum and bispectrum
over all length scales where the input halo properties are valid. It also
provides a physical interpretation of the clustering properties of matter in
the universe.Comment: Final version to appear in the Astrophysical Journal 544 (2000).
Minor revisions; 1 additional figure. 25 pages with 6 inserted figure
Dynamic quantum clustering: a method for visual exploration of structures in data
A given set of data-points in some feature space may be associated with a
Schrodinger equation whose potential is determined by the data. This is known
to lead to good clustering solutions. Here we extend this approach into a
full-fledged dynamical scheme using a time-dependent Schrodinger equation.
Moreover, we approximate this Hamiltonian formalism by a truncated calculation
within a set of Gaussian wave functions (coherent states) centered around the
original points. This allows for analytic evaluation of the time evolution of
all such states, opening up the possibility of exploration of relationships
among data-points through observation of varying dynamical-distances among
points and convergence of points into clusters. This formalism may be further
supplemented by preprocessing, such as dimensional reduction through singular
value decomposition or feature filtering.Comment: 15 pages, 9 figure
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