4.8 Towards Probing the Mass Spectrum of Gravitational Structures With Weak Lensing

4.8.1 Mapping Large Scale Structures

The detection of weak shear down to the 5% level in Q2345+007 (Bonnet et al. 1993) field and on Mpc scales in Cl0024+1654 (Bonnet et al. 1994) is the first observational step toward the mapping of larger structures. The basic theoretical ideas which support such an investigation were presented about two decades ago. Seminal works by Kristian & Sachs (1966), Gunn (1967) and Kristian (1967) predicted that any anisotropy in the universe and any gravitational structures should perturb the light path of photons and induce gravitational distortion of the images of distant galaxies. Later, Blandford and Jaroszynsky (1981) analyzed the gravitational distortion of distant radiosources by clusters of galaxies. Webster (1985) also calculated the distribution of the distortion of background galaxies around clusters and found that for circular sources, the ellipticity should increase with the redshift of sources. This effect was expected to be detected from the statistical analysis of the orientation and ellipticity of distant galaxies.

Figure 20. Effect of gravitational distortion by a large scale structure with a gravity field oriented along the left-right diagonal: from left to right the intensity of the deflector starts at zero and slowly increases. We clearly observe an increase of the correlation of orientation and ellipticity, even for a small shear. This effect should be detectable provided the resolution window on the sky is large enough (inspired from Blandford et al. 1991).

The first observations were done with photographic plates by Kristian (1967), who attempted to measure shapes of galaxies near clusters of galaxies, and later by Valdes, Tyson & Jarvis (1983) who measured the coherent shear of a complete sample of galaxies ranging from J = 22 to J = 23.5. At these early times Kristian did not detect any shear and Valdes et al. also failed to observe coherent alignment and ellipticity although they surveyed more than 44,000 galaxies.

In spite of these discouraging early observational results, numerical simulations have been done to address the effects of propagating ray bundles in inhomogenous universes and the resulting distortion and amplification of background sources. Schneider & Weiss (1988) and Babul & Lee (1991) concluded that the cumulative shear of smooth structures should have non-negligible effects on the ellipticities of sources. But results from Jarosczynski et al. (1990), or Bartelemann & Schneider (1991) reveal that the effect is small and probably at the limits of present-day observational techniques. However, more recent theoretical models of large scale structures suggest that the analysis of shear effects requires careful treatment of the non-linear regime for the growth of structures from initial density fluctuations. In particular, the adhesion approximation predicts larger distortion than the Zel'dovich approximation (Bartelemann & Schneider 1992). Fortunately, the discovery of arclets in A370 (Fort et al. 1988), A1689 and 3C295 (Tyson, Valdes and Wenk 1990), and the first detection of giant structures larger than 100 Mpc, such as the Great Wall (Geller and Huchra 1989), motivated Miralda-Escudé (1991b), Blandford et al. (1991) and Kaiser (1992) to revisit the topic and to encourage observers to reconsider the possibility of detecting very weak shear with the new and more efficient observational tools at our disposal (large telescopes with sub-arcsecond seeing, HST and large CCD mosaics). They gave compelling theoretical evidence that weak shears should be measurable if the low signal to noise of an individual distorted galaxy is increased by co-adding the signal of a large number of distant galaxies within a large resolution window on the sky (Fig. 20). This idea was strongly motivated by the detection of a large population of distant galaxies by Tyson (1988), which offers the ideal grid of sources for which to map the shear from large scale structures of the universe. With a projected number density of about 100 arcmin^-2, Tyson's population fills the sky and should probe density contrasts of about 3 x 10^-3 with a spatial resolution of 1 degree (Blandford et al. 1991). The weak shear detection by Bonnet et al. (1994) in the outermost region of a rich cluster corresponds to a value of 5 x 10^-2 for a superpixel of about 1 arcmin². Similar values are obtained by Fahlman et al. (1994) and Smail et al. (1994b). Therefore, if the random error of the ellipticity varies as the square root of the number of sources within the superpixel and if the shear can be properly corrected for instrumental errors, the Blandford et al. prediction could be checked. One could search over correlation lengths of a few degrees for the alignment of the distant galaxies. This will allow us to probe the distribution of dark matter for a lens redshift in the range 0.2 - 0.4 up to 100 Mpc scales. Unfortunately the discouraging problems that the observers have to confront is that even with the largest CCD mosaics such a survey will require a dedicated large telescope with excellent seeing during a large fraction of the observing time. An alternative approach would be to sample the shear on some selected lines of sight where we already suspect a reasonable amount of shear. The best candidate fields are those where we already suspect a magnification bias of distant radiosources.