The Gravitational Lensing in Redshift-space Correlation Functions of Galaxies and Quasars

The gravitational lensing, as well as the velocity field and the cosmological light-cone warp, changes the observed correlation function of high-redshift objects. We present an analytical expression of 3D correlation function, simultaneously including those three effects. When two objects are separated over several hundreds Mpc along a line of sight, the observed correlation function is dominated by the effect of gravitational lensing rather than the intrinsic clustering. For a canonical lambda-CDM model, the lensing signals in the galaxy-galaxy and galaxy-QSO correlations are beyond noise levels in large-scale redshift surveys like the Sloan Digital Sky Survey.Comment: 10 pages, 1 figure, submitted to ApJ

Testing a new analytic model for gravitational lensing probabilities

We study gravitational lensing with a multiple lens plane approach, proposing a simple analytical model for the probability distribution function (PDF) of the dark matter convergence, kappa, for the different lens planes in a given cosmology as a function of redshift and smoothing angle, theta. The model is fixed solely by the variance of kappa, which in turn is fixed by the amplitude of the power spectrum, sigma_8. We test the PDF against a high resolution Tree-Particle-Mesh simulation and find that it is far superior to the Gaussian or the lognormal, especially for small values of theta << 1 arcmin and at large values of kappa relevant to strong lensing. With this model, we predict the probabilities of strong lensing by a single plane or by multiple planes. We find that for theta ~ 10 arcsec, a single plane accounts for almost all (~ 98%) of the strong lensing cases for source redshift unity. However, for a more typical source redshift of 4, about 12% of the strong lensing cases will result from the contribution of a secondary clump of matter along the line of sight, introducing a systematic error in the determination of the surface density of clusters, typically overestimating it by about 2-5%. We also find that matter inhomogenieties introduce a dispersion in the value of the angular diameter distance about its cosmological mean. The probable error relative to the mean increases with redshift to a value of about 8% for z ~ 6 and theta ~ 10 arcsec.Comment: Accepted for publication in ApJ, 13 pages, 12 figures, revised version, references added, section 6 expande

Cosmological Model Predictions for Weak Lensing: Linear and Nonlinear Regimes

Weak lensing by large scale structure induces correlated ellipticities in the images of distant galaxies. The two-point correlation is determined by the matter power spectrum along the line of sight. We use the fully nonlinear evolution of the power spectrum to compute the predicted ellipticity correlation. We present results for different measures of the second moment for angular scales \theta \simeq 1'-3 degrees and for alternative normalizations of the power spectrum, in order to explore the best strategy for constraining the cosmological parameters. Normalizing to observed cluster abundance the rms amplitude of ellipticity within a 15' radius is \simeq 0.01 z_s^{0.6}, almost independent of the cosmological model, with z_s being the median redshift of background galaxies. Nonlinear effects in the evolution of the power spectrum significantly enhance the ellipticity for \theta < 10' -- on 1' the rms ellipticity is \simeq 0.05, which is nearly twice the linear prediction. This enhancement means that the signal to noise for the ellipticity is only weakly increasing with angle for 2'< \theta < 2 degrees, unlike the expectation from linear theory that it is strongly peaked on degree scales. The scaling with cosmological parameters also changes due to nonlinear effects. By measuring the correlations on small (nonlinear) and large (linear) angular scales, different cosmological parameters can be independently constrained to obtain a model independent estimate of both power spectrum amplitude and matter density \Omega_m. Nonlinear effects also modify the probability distribution of the ellipticity. Using second order perturbation theory we find that over most of the range of interest there are significant deviations from a normal distribution.Comment: 38 pages, 11 figures included. Extended discussion of observational prospects, matches accepted version to appear in Ap

The Origin of the Brightest Cluster Galaxies

Most clusters and groups of galaxies contain a giant elliptical galaxy in their centres which far outshines and outweighs normal ellipticals. The origin of these brightest cluster galaxies is intimately related to the collapse and formation of the cluster. Using an N-body simulation of a cluster of galaxies in a hierarchical cosmological model, we show that galaxy merging naturally produces a massive, central galaxy with surface brightness and velocity dispersion profiles similar to observed BCG's. To enhance the resolution of the simulation, 100 dark halos at $z=2$ are replaced with self-consistent disk+bulge+halo galaxy models following a Tully-Fisher relation using 100000 particles for the 20 largest galaxies and 10000 particles for the remaining ones. This technique allows us to analyze the stellar and dark matter components independently. The central galaxy forms through the merger of several massive galaxies along a filament early in the cluster's history. Galactic cannibalism of smaller galaxies through dynamical friction over a Hubble time only accounts for a small fraction of the accreted mass. The galaxy is a flattened, triaxial object whose long axis aligns with the primordial filament and the long axis of the cluster galaxy distribution agreeing with observed trends for galaxy-cluster alignment.Comment: Revised and accepted in ApJ, 25 pages, 10 figures, online version available at http://www.cita.utoronto.ca/~dubinski/bcg

Ray Tracing Simulations of Weak Lensing by Large-Scale Structure

We investigate weak lensing by large-scale structure using ray tracing through N-body simulations. Photon trajectories are followed through high resolution simulations of structure formation to make simulated maps of shear and convergence on the sky. Tests with varying numerical parameters are used to calibrate the accuracy of computed lensing statistics on angular scales from about 1 arcminute to a few degrees. Various aspects of the weak lensing approximation are also tested. For fields a few degrees on a side the shear power spectrum is almost entirely in the nonlinear regime and agrees well with nonlinear analytical predictions. Sampling fluctuations in power spectrum estimates are investigated by comparing several ray tracing realizations of a given model. For survey areas smaller than a degree on a side the main source of scatter is nonlinear coupling to modes larger than the survey. We develop a method which uses this effect to estimate the mass density parameter Omega from the scatter in power spectrum estimates for subregions of a larger survey. We show that the power spectrum can be measured accurately from realistically noisy data on scales corresponding to 1-10 Mpc/h. Non-Gaussian features in the one point distribution function of the weak lensing convergence (reconstructed from the shear) are also sensitive to Omega. We suggest several techniques for estimating Omega in the presence of noise and compare their statistical power, robustness and simplicity. With realistic noise Omega can be determined to within 0.1-0.2 from a deep survey of several square degrees.Comment: 59 pages, 22 figures included. Matches version accepted for Ap

Warped Galaxies From Misaligned Angular Momenta

A galaxy disk embedded in a rotating halo experiences a dynamical friction force which causes it to warp when the angular momentum axes of the disk and halo are misaligned. Our fully self-consistent simulations of this process induce long-lived warps in the disk which mimic Briggs's rules of warp behavior. They also demonstrate that random motion within the disk adds significantly to its stiffness. Moreover, warps generated in this way have no winding problem and are more pronounced in the extended \h1 disk. As emphasized by Binney and his co-workers, angular momentum misalignments, which are expected in hierarchical models of galaxy formation, can account for the high fraction of warped galaxies. Our simulations exemplify the role of misaligned spins in warp formation even when the halo density is not significantly flattened.Comment: 6 pages, 5 figures. Accepted for publication in Ap.J.