Detection of Weak Gravitational Lensing by Large-scale Structure

TL;DR

This study presents a ground-based detection of cosmic shear from weak gravitational lensing by large-scale structure, demonstrating a 3.4σ signal via careful PSF correction and extensive simulations. By modeling the distortion matrix and the shear power spectrum, it links observed ellipticities to the mass power spectrum and constrains σ8 within a ΛCDM framework (Ω_m ≈ 0.3) using a median source redshift around z_s ≈ 0.8. The work shows that ground-based surveys can measure the mass distribution on multiple scales, with cosmic variance currently dominating uncertainties; future, larger field sets will tighten cosmological constraints and enable power-spectrum shape measurements. It rules out COBE-normalised SCDM at ~3σ and provides σ8 ≈ 1.5 ± 0.5 for the ΛCDM model, consistent with cluster abundances and highlighting the value of cosmic shear as a robust, bias-free probe of structure formation.

Abstract

We report a detection of the coherent distortion of faint galaxies arising from gravitational lensing by foreground structures. This ``cosmic shear'' is potentially the most direct measure of the mass power spectrum, as it is unaffected by poorly-justified assumptions made concerning the biasing of the distribution. Our detection is based on an initial imaging study of 14 separated 8' x 16' fields observed in good, homogeneous conditions with the prime focus EEV CCD camera of the 4.2m William Herschel Telescope. We detect an rms shear of 1.6% in 8' x 8' cells, with a significance of 3.4 sigma. We carefully justify this detection by quantifying various systematic effects and carrying out extensive simulations of the recovery of the shear signal from artificial images defined according to measured instrument characteristics. We also verify our detection by computing the cross-correlation between the shear in adjacent cells. Including (gaussian) cosmic variance, we measure the shear variance to be (0.016)^2 plus/minus (0.012)^2 plus/minus (0.006)^2, where these 1 sigma errors correspond to statistical and systematic uncertainties, respectively. Our measurements are consistent with the predictions of cluster-normalised CDM models (within 1 sigma) but a COBE-normalised SCDM model is ruled out at the 3.0 sigma level. For the currently-favoured Lambda-CDM model (with Omega_m = 0.3), our measurement provides a normalisation of the mass power spectrum of sigma_8 = 1.5 plus/minus 0.5, fully consistent with that derived from cluster abundances. Our result demonstrates that ground-based telescopes can, with adequate care, be used to constrain the mass power spectrum on various scales. The present results are limited mainly by cosmic variance, which can be overcome in the near future with more observations.

Figures (13)

• Figure 1: Shear power spectrum for each cosmological model and for sources at $z_{s}=1$. Note that the SCDM spectrum is larger due to its higher normalisation.
• Figure 2: Dependence of the rms shear on the source redshift $z_{s}$ and the power spectrum normalisation $\sigma_{8}$. The cell was chosen to be a square of side $\alpha=8'$.
• Figure 3: Example reduced image (CIRSI2); the field of view is 8'$\times$ 16'. Note that in our analysis, we divide each such field into two 8' $\times$ 8' cells.
• Figure 4: Expected (top) and measured (bottom) instrumental shear pattern for the WHT Prime Focus. The expected pattern was derived from the distortion model given in the WHT Prime Focus manual (Carter & Bridges 1995). The observed pattern was measured using 3 astrometric frames in one of our fields.
• Figure 5: Top: Stellar ellipticity distribution for the field of figure \ref{['fig:cirsi2']} (CIRSI2). The mean value observed is $\bar{e}^{*} \simeq 0.07$. Bottom: Residual stellar ellipticity after correction. The residual mean ellipticity is $\bar{e}^{res} \simeq 2.6 \times 10^{-3}$.