Nick Kaiser

Excursion set mass functions for hierarchical Gaussian fluctuations

Most schemes for determining the mass function of virialized objects from the statistics of the initial density perturbation field suffer from the «cloud-in-cloud» problem of miscounting the number of low-mass clumps, many of which would have been subsumed into larger objects. We propose a solution based on the theory of the excursion sets of F(r, R f ), the four-dimensional initial density perturbation field smoothed with a continuous hierarchy of filters of radii Rf. We identify the mass fraction of matter in virialized objects with mass greater than M with the fraction of space in which the initial density contrast lies above a critical overdensity when smoothed on some filter of radius greater than or equal to R f (M).

On the Spatial correlations of Abell clusters

If rich clusters formed where the primordial density enhancement, when averaged over an appropriate volume, was unusually large, then they give a biased measure of the large-scale density correlation function determiend by the probability distribution of the density fluctuations on a rich cluster mass scale. If this distribution was Gaussian, the correlation function is amplified. The amplification for rich clusters is estimated to be eaual about ten and predicted trend of amplification with richness agrees qualitatively with that observed. Some implications of these results for the large-scale density correlations are discussed.

POWER-SPECTRUM ANALYSIS OF THREE-DIMENSIONAL REDSHIFT SURVEYS

We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting scheme under the reasonable (and largely empirically verified) assumption that the long wavelength Fourier components are Gaussian distributed. We apply the formalism to the updated 1-in-6 QDOT IRAS redshift survey, and compare our results to data from other probes: APM angular correlations; the CfA and the Berkeley 1.2Jy IRAS redshift surveys. Our results bear out and further quantify the impression from e.g.\ counts-in-cells analysis that there is extra power on large scales as compared to the standard CDM model with

Weak gravitational lensing of distant galaxies

\Omega h\simeq 0.5

Mapping the dark matter with weak gravitational lensing

. We apply likelihood analysis using the CDM spectrum with

Science Objectives and Early Results of the DEEP2 Redshift Survey

\Omega h

Evolution of clusters of galaxies

as a free parameter as a phenomenological family of models; we find the best fitting parameters in redshift space and transform the results to real space. Finally, we calculate the distribution of the estimated long wavelength power. This agrees remarkably well with the exponential distribution expected for Gaussian fluctuations, even out to powers of ten times the mean. Our results thus reveal no trace of periodicity or other non-Gaussian behavior.

The Pan-STARRS1 Photometric System

We analyze the two-point statistics of the gravitationally induced ellipticities of distant images whick provide a direct probe of the mass fluctuation spectrum P(k). The analysis extends previous work in the following respects : (1) We explore the relation between the ellipticity pattern of the background galaxies and the projected density of foreground matter. (2) We calculate angular power spectra, using the analogue of Limbers equation in the Fourier domain, as well as angular correlation functions. (3) The analysis is valid for arbitrary evolution of P(k) and for an arbitrary distance distribution for the galaxies

The Deep Evolutionary Exploratory Probe 2 Galaxy Redshift Survey: The Galaxy Luminosity Function to z ~ 1*

We consider the problem of reconstructing the projected mass distribution in clusters from coherent distortions of background galaxies. The ellipticity of a background galaxy provides an estimate of the trace-free components of the tidal field ∂ 2 Φ/∂θ y ∂θ j where Φ(θ) is the two-dimensional potential generated by the surface density Σ(θ). We present a technique for inverting this problem. The resulting surface density contains a strong, but incoherent, random component arising from the random intrinsic galaxy ellipticities. This can be removed by filtering

The DEEP2 Galaxy Redshift Survey: Design, Observations, Data Reduction, and Redshifts

The DEIMOS spectrograph has now been installed on the Keck-II telescope and commissioning is nearly complete. The DEEP2 Redshift Survey, which will take approximately 120 nights at the Keck Observatory over a three year period and has been designed to utilize the power of DEIMOS, began in the summer of 2002. The multiplexing power and high efficiency of DEIMOS enables us to target 1000 faint galaxies per clear night. Our goal is to gather high-quality spectra of ≈ 60,000 galaxies with z>0.75 in order to study the properties and large scale clustering of galaxies at z ≈ 1. The survey will be executed at high spectral resolution, R=λ/Δλ ≈ 5000, allowing us to work between the bright OH sky emission lines and to infer linewidths for many of the target galaxies (for several thousand objects, we will obtain rotation curves as well). The linewidth data will facilitate the execution of the classical redshift-volume cosmological test, which can provide a precision measurement of the equation of state of the Universe. This talk reviews the project, summarizes our science goals and presents some early DEIMOS data.