5.1 Giant Arcs
Smail et al. (1991) analyzed the spatial distribution of arc candidates (elongated objects with a/b > 2) in a sample of 19 rich distant clusters and explored the possibility of using arc imaging to derive the redshift distribution of distant galaxies without spectroscopic data. Assuming clusters are singular isothermal spheres with the velocity dispersion of the cluster galaxies and a flat universe, Smail et al. tested two extreme redshift distributions of faint flat spectrum galaxies (most are at low redshift, or all are at very high redshift). They compared the number and the radial distribution of arcs with the results predicted by simulations for the two hypotheses. They showed that the skewness of the profile of the distribution of arc redshifts could be used to constrain the redshift distribution of the sources. They verified that the shapes and orientations of arc candidates are statistically consistent with the gravitational lens hypothesis, even though they do not have redshifts for all of these arcs. Unfortunately, as was already stressed by Fort (1989), since the number of arc(let)s depends on the fourth power of the velocity dispersion, a small error in cl changes dramatically the results for the number and angular scale of the distribution of arc(let)s. Indeed Smail et al. concluded that it is difficult to infer the source redshift distribution without precise information on the cluster velocity dispersion. Furthermore, this procedure demands a good knowledge of the cluster center. Departures from spherical symmetry, the existence of substructures which could locally change the shapes of arcs, and the intrinsic ellipticity of background sources can also strongly perturb the magnification of arcs and their distance to the cluster center.
The source redshift distribution and spectral energy distribution can also be directly analyzed from the spectroscopy and multicolor photometry of the brightest giant arcs. To date we know the redshifts of about 10 arcs (Fig. 9). Most spectroscopic and photometric data show that arcs have flat spectra with a frequent occurrence of emission lines (Mellier et al. 1991). Although some have large redshifts there is a clear trend for redshifts lower than 1. The spectrophotometry of arcs is consistent with the results of the deepest redshift surveys (Colless et al. 1990, 1993; Lilly 1993, Tresse et al. 1993). Smail et al. (1993) have analyzed star formation in the brightest giant arcs by using optical spectra and multi-band photometry from B to K. The study confirms that most arcs are intrinsically very blue but the stellar content cannot correspond to a single burst which occurs during the galaxy formation. It also cannot be interpreted as arising from old galaxies undergoing a secondary starburst. Instead, giant arcs favor the hypothesis that star formation in galaxies extends continuously from z 1 until now. Some arcs are clearly clumpy and they may be the magnified images of young merging galaxies. The understanding of the nature of these flat spectrum galaxies is a problem that will need further investigating.
The first observations of a velocity gradient in the arc in A2390 by Pelló et al. (1991) prove that large magnifications make rotation curves of very distant spiral galaxies observable. Soucail & Fort (1991) and Narasimha & Chitre (1993) first emphasized that spectroscopic observations and multiwaveband photometry of distant arcs give an opportunity to test the validity of the Tully-Fisher relation for galaxies with z > 1. The equivalent resolution of the source along the tangential magnification axis can reach 0.05 arcsec with ground based observations and 10 times this value with future HST observations. Observations of rotation curves of small distant galaxies in this way seem promising for the understanding of the dynamical evolution of spirals, formation of their dark halos and possibly their use as distance indicators on the largest cosmological scales.
Miralda-Escudé (1993b) also emphasized that arc statistics can be used to constrain the angular sizes of distant background sources. This can be understood rather easily because it is expected that large sources need lower amplification to make an giant arc with a fixed length. Using spherical isothermal deflectors, Miralda-Escudé tentatively predicted that sources should have angular sizes larger than 0.5", in good agreement with deep imaging of faint galaxies (Lilly, Cowie & Gardner 1991). These preliminary results are interesting but are based on a small sample of arcs. Therefore, they need further confirmation on a well-defined sample of clusters of galaxies observed in similar seeing and photometric conditions.