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3.1 Imaging and Photometry of Arcs

The present X-ray samples based on the Extended Medium Sensitivity Survey, or luminous X-ray Abell clusters (Gioia et al. 1990) converge toward the following statistics (see Fort 1992, Luppino et al. 1993): for very rich, X-ray luminous clusters having LX > 5 x 1044, erg/s the probability of finding a large arc is about 30% up to the surface brightness detection limit of B = 28 / square arcsec (altogether, about 100 clusters have been surveyed and 32 arcs discovered). New surveys based on well defined ROSAT cluster samples are now in progress and should provide a good estimate of the frequency of arc occurrence in the near future. Therefore, we a priori know where to find gravitational arcs with a probability of success much higher than preliminary predictions (Nemiroff & Dekel 1989). At present the discovery rate could be about one per night of observing time on a large telescope. However, the detection rate strongly depends on the image quality of the site, and it is difficult to define an homogeneous sample based on multi-site observations. Typically, multicolor photometry of arc(let)s with a 4 meter telescope requires a minimum of 3 hours exposure time with the shift and add technique (Tyson 1988) and seeing below 0.8 arcsec. Clearly, the CFHT has the highest detection rate as compared with any other 4-m class telescope, but everywhere seeing effects probably prevent the detection of very faint thin arcs. The Durham-Cambridge group obtained HST images of A370 and Cl0024+1654 (Ellis, private communication), before its refurbishment. These impressive images are convincing evidence of the scientific interest of very high spatial resolution. Most of the groups which are active in arc surveys will soon be involved in future HST observations, now that it has been successfully refurbished.

Basically, arcs can be separated into four categories:

1. Fold arcs correspond to most of the giant curved arcs, and it is possible to identify 2 subcomponents with reversed parity, and eventually, some other extended counter images. Cl2244-02 is the archetype of this configuration (Hammer et al. 1989, and Fig. 13). MS2137-23 (Fort et al. 1992), MS0440+02 (Luppino et al. 1993), Q0957+561 (Bernstein et al. 1993) are also fold arcs.

2. Cusp arcs correspond to giant arcs with three segments clearly visible. The most spectacular are Cl0024+1654 (Kassiola, Kovner & Fort 1992), A370 (Kneib et al. 1993). Cl0500-24 (Giraud 1988) and A1942 (Smail et al. 1991) might belong to this category.

In fact it is not always easy to discriminate fold arcs from cusp arcs because the source may be just across the caustic line. It may result in strange merging images, where each half of the source has a different number of multiple images.

3. Straight ``arc'' configurations may correspond to lip caustics generated by galaxy members embedded in the general halo of the cluster or to beak-to-beak configurations of caustics generated by bimodal clusters with the arc located on the saddle. This kind of arc is relatively frequent, which means that clusters are often multi-component systems. A2390 (Pelló et al. 1991) was the first straight arc detected. It was extensively discussed by Kassiola, Kovner & Blandford (1992). They could not find simple lens configurations to explain the arc and suggested that it could be a beak-to-beak model involving two lensed sources and a secondary dark potential. MS0302+17 (Mathez et al. 1992), Cl2236 (Melnick et al. 1992) and possibly Cl0500-24 (Giraud 1988, Wambsganns et al. 1989) seem to be produced in the saddle of a bimodal potential.

4. A large number of arcs have not been observed in good seeing conditions, and we cannot detect any substructures along the arc which could help in classification. There are also some peculiar cases with good images which do not correspond to a simple lens configuration. S295 (Leborgne et al. 1994 in preparation, Mellier et al. 1994 in preparation) is a good example. Note also the arc observed by Bonnet et al. (1993) in the field of the doubly- imaged quasar Q2345+007 which is not apparently associated with an optical cluster. Nevertheless, it is quite striking that the geometries of most of the observed cases are similar to the predictions for elliptical models (Kovner 1988). Note also, that if clusters are just below the critical mass density, they have lip caustics. They also split and magnify images which cannot be easily distinguished from straight arcs (Kovner 1987c). We do not know the actual occurrence of such cases of marginal lenses. In fact, several straight arclets associated with bright galaxy members like the ones in A2390 could be due to such secondary lip caustics.

The histogram of clusters with arcs and arclets (Fig. 9) shows a clear peak between z = 0.2 and z = 0.4. The strong cut-off above z = 0.4 can have multiple interpretations: (1) observational bias in cluster selection. It is remarkable that this cut-off is the same as for the Abell (1958) and Abell, Corwin & Olowin (1989) cluster catalogs; (2) the number density of faint distant galaxies decreases at high-z for the limiting magnitudes reached by the observations (B = 27); (3) or strong evolution of the projected surface mass density of clusters of galaxies with redshift. Since these effects can mix together, additional observations from X-ray satellites, deep redshift surveys of faint galaxies, and complete redshift surveys of distant clusters are needed.

Figure 9. Redshift distribution of clusters with arc(let)s (white boxes) and arcs (filled boxes). The cluster is referenced with each box. Note the strong peak between z = 0.2 and z = 0.4. Only one third of the arc(let)s have redshifts (Table 1).

Although the occurrence of arcs seems rather well understood and almost compatible with the density of background galaxies, some of the richest clusters do not display arcs on the deepest images (Fort 1989). In some cases arclets are present in a particular quadrant around the clusters. The distant cluster Cl0016+16 (z = 0.56) is one of these cases. This is one of the richest known distant clusters and the strongest X-ray emitter. It is rather extended on the sky, so the light from many background sources should cross this cluster. Neither arcs, nor arclets have been seen so far, although deep CCD images in good seeing conditions have been obtained at the CFHT (Mellier 1992 unpublished). However, Smail et al. (1994b) may have detected weak gravitational shear. It would be very interesting to go even deeper and extend the observations to the outermost regions in order to confirm this result. We do not know which fraction of moderate-redshift clusters have no arclets at all, and indeed no clear understanding of this lack of detection. Several explanations can be considered: some kind of absorption prevents the visibility of background sources; the distribution of distant sources is more clumpy than generally accepted from the study of field galaxies and the cluster is ``lensing'' a blank field; the arclets are formed at a distance from the center of the cluster outside the CCD field (CCDs used during the first arc surveys have a field of view of only 2 x 3 arcmin); the cluster does not have the critical surface density and is just a superimposition of several clumps of galaxies along the line of sight. It is quite clear that it would be extremely valuable to clarify these cases with a measure of the very weak shear around these clusters (cf section 4.4).

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