The distortion of distant galaxy images by large-scale structure

Inhomogeneity in the distribution of mass in the universe on scales ≲ 100 Mpc can generate a coherent shear distortion or polarization of the images of background galaxies. This distortion may be measurable over patches of the sky up to a few square degrees in size. If this distortion is measured, or conversely, if its magnitude is limited, it should help us understand the degree to which luminosity traces the underlying mass over cosmological scales. A prescription is given for quantifying the galaxy distortion and a propagation equation for its evolution in an inhomogeneous universe is derived. The creation of shear by inhomogeneity is illustrated using model kinematic universes comprising random distributions of point masses, spheres and circular discs designed to simulate the superclusters, voids and ‘walls’ reported in galaxy velocity surveys. Using these simulations, we estimate that an rms induced ellipticity of |p|_(rms) ˜ 0.2Ω_(LSS) (where Ω_(LSS) is the fraction of the mass of the universe clustered on the large scale) will be produced. The angular correlation length is ˜ 1.6°. In an alternative prescription, the universe is modelled using a power spectrum of density fluctuations and the mean correlation function is computed both analytically and numerically. In these simulations we find that |p|_(rms) ˜0.02 for biased cold dark matter models of an Einslein–De Sitter universe, and the effective correlation length is θ_(1/2) ˜ 0.5^ΰ. For a hot dark matter dominated universe the correlation length is θ_(1/2) ˜ 0.7^ΰ. The faint, blue galaxies discovered by Tyson and collaborators have a surface density of ˜ 3 × 10^5 deg^(−2) and should provide an ideal set of sources for measuring this effect