Abstract
Blind surveys for distant galaxies, which by their nature are very faint, have uncovered relatively few galaxies beyond a redshift of z ~ 8. Furthermore, because these galaxies are too faint for spectroscopy, their redshifts are inferred through fitting model galaxy templates to their spectral energy distributions (photometric redshifts). By comparison, with the aid of gravitational lensing by galaxy clusters, which boost the brightness of background lensed galaxies, a relatively large number of faint galaxies having photometric redshifts as high as z ~ 11 have been found. The redshifts of these galaxies can also be determined purely through geometry (geometric redshifts), provided that an accurate model of the foreground lensing cluster is constructed. Here we infer the geometric redshift to the triply-lensed galaxy (MACS0647-JD) which remains the most distant galaxy candidate observed by lensing. The photometric redshift of this galaxy provides an ambiguous solution both at z ~ 2:5 and z ~ 10.7. Using 9 sets of lensed images, we reconstructed a robust mass model of the cluster MACS0647. The accuracy of this mass model has been evaluated by internal consistency checks, which show that it could reproduce the observed positions and relative brightnesses of multiply-lensed images. With this mass model we predicted a geometric redshift of MACS0647-JD at z ~ 10:8. This is currently the most distant galaxy that its redshift is purely confirmed by geometry.
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