Annu. Rev. Astron. Astrophys. 2000. 38: 667-715
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4.10. Gravitational Lensing

The depths of the HDFs have made them well suited for studies of gravitational lensing. As [Blandford1998] noted in his review, based on a rule of thumb from the number of lensed quasars and radio sources in other surveys, roughly 0.2 % of the galaxies, corresponding to five to ten sources, were expected to be strongly lensed (producing multiple images) in each HDF field. In addition, weak lensing by large-scale structure and individual galaxies should slightly distort most of the galaxy images. Initial visual inspection of the HDFs produced a number of possible strong lensing candidates [Hogg et al. 1996, Barkana et al. 1999], but none has yet been confirmed by spectroscopy. Rather, a few of the brighter examples appear not to be lensed systems, but only chance superpositions [Zepf et al. 1997]. A few candidates remain in each of the primary WFPC2 HDF fields [Barkana et al. 1999], but it will require spectroscopy of very faint sources to confirm their nature.

An analysis of the HDF-N images by [Zepf et al. 1997] concluded that there were at most one to two strongly lensed sources in the entire field, although very faint objects with small angular separation could have escaped detection. On this basis they suggested that the HDF data were not compatible with a large cosmological constant. [Cooray et al. 1999] took this further by utilizing published photometric redshifts for the galaxies in the HDF-N to calculate the expected number of multiply imaged galaxies in the field. They found that a limit of one detectable strongly lensed source requires OmegaLambda - OmegaM < 0.5. For OmegaM, OmegaLambda, Omegatot = 0.3, 0.7, 1 they predict 2.7 multiply imaged galaxies. The lensing statistics are thus, in spite of earlier expectations for a larger number of lenses, not in conflict with recent determinations of OmegaLambda from high-redshift SN [Perlmutter et al. 1999, Riess et al. 1998].

Weak lensing is manifested by a tangential shear in the image of the more distant source, and the amount of ellipticity, or polarization p, introduced by a typical closely-spaced galaxy pair is of the order of p ~ 10-2. It is possible to attempt a statistical detection by looking for the effect superimposed on the intrinsic morphologies of the source galaxies perpendicular to galaxy-galaxy lines of sight. As a differential effect, weak-lensing distortion is far less sensitive to the cosmological model than to the masses or surface densities of the intervening deflector galaxies. Using color and brightness as redshift indicators, [Dell'Antonio & Tyson 1996] defined a sample of 650 faint background and 110 lens galaxies in the HDF-N and reported a 3sigma detection equivalent to p = 0.06 for galaxy-lens pairs having a separation of 2". This corresponds to an average galaxy mass of 6 × 1011 Modot inside 20 kpc, or an internal velocity dispersion of 185 km s-1 A similar analysis of HDF-N images was subsequently performed by [Hudson et al. 1998], who used photometric redshifts to determine distances of lens and source galaxies, and who discriminated between lensing galaxy types based on colors. Limiting their analysis to separations greater than 3", they succeeded in measuring background shear at a 99% confidence level, finding that intermediate-redshift spiral galaxies follow the Tully-Fisher relation but are 1 mag fainter than local spirals at fixed circular velocity. Although the sense of the evolution is the opposite of that found in the kinematical studies, given the uncertainties the lensing result is consistent with the modest luminosity-evolution observed by [Vogt et al. 1997] when the studies are compared using the same cosmology. The lensing results are inconsistent with the larger luminosity evolution found by [Rix et al. 1997] and [Simard & Pritchet 1998].

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