Redshifts of Faint Blue Galaxies From Gravitational Lensing

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Abstract
The possibility to reconstruct cluster mass distributions from their gravitational lensing effects on background sources is now firmly established and is discussed in a number of other contributions to these proceedings. Here, we want to suggest a new method, the parallax method (Bartelmann & Narayan 1995), to infer the redshifts of the background sources, which are in general too faint to allow spectroscopy. The method is based on gravitational lensing, and apart from arclet redshifts it yields calibrated, accurate cluster reconstructions. The key idea is simple and rests on three facts: (1) The strength of lensing effects increases with source redshift, if the redshift is kept fixed. (2) The surface brightness of the arclet sources steeply decreases with redshift z. Neglecting spectral effects, the surface brightness is ∝ (1 + z)−4. (3) The surface brightness of the sources is invariant to lensing. In combination, these facts imply that lensing effects become stronger with decreasing surface brightness, so that relative distances of arclet sources can be inferred from the variation of lensing effects with the surface brightness of lensed sources. If the redshift of the brightest sources can be measured spectroscopically, the relative distances can be calibrated and the average redshift as a function of surface brightness can be found.