8 Summary and conclusions

We have presented the results of our systematic search for lensed arcs and arclets in a large, homogeneous, X-ray-selected sample of 38 distant clusters of galaxies. Below, we summarize our conclusions.

1.

Our survey has yielded 8 clusters with giant arcs, 2 clusters with arclets, and 6 candidate lensing systems.

2.

Our results indicate that high X-ray luminosity ($L_{\rm x}$$\,\gt\,$4 10⁴⁴ ergs^-1) does indeed identify the most massive clusters, and thus X-ray selection is the preferred method for finding true, rich clusters at intermediate and high redshifts.

3.

The majority of the arcs in our sample have large axis ratios, are thin, and in those clusters with obvious optical axes of symmetry, the arcs tend to be oriented orthogonal to the optical major axis. Furthermore, the high lensing frequency in our sample (21% giant arcs in the entire sample, 30% giant arcs for clusters with $L_{\rm x}$$\,\gt\,$4 10⁴⁴ ergs^-1, 60% for clusters with $L_{\rm x}$$\,\gt\,$1$\linebreak$10⁴⁵ ergs^-1) is consistent with the lensing frequency predicted by statistical models that assume clusters have compact cores.

However, our conclusion that the central regions of these clusters have compact mass density profiles does not preclude the presence of large, extended dark matter halos that is convincingly demonstrated to exist through the detection of weak lensing at large radii (Smail et al.1994; Kaiser et al.1996; Squires et al.1997; Geiger & Schneider 1998; Clowe et al.1998; Kaiser et al.1998).

Future observations and theoretical modelling will provide important information on these cluster lenses. We are presently acquiring optical spectra of the clusters and arcs with the CFHT and Keck telescopes in order to measure the arc redshifts and the cluster velocity dispersions. These spectra will allow us to confirm the lensing hypothesis, especially for the candidate arcs and arclets, and will be crucial for theoretical modelling of the more interesting lensing configurations.

Acknowledgements

We thank the UH Time Allocation Committee for their generous allocation of UH 2.2m and CFHT time for this project. We also thank John Stocke and Simon Morris for sharing their data, particularly the MS0451-03 redshift, prior to publication. We have enjoyed fruitful discussions and interactions with Megan Donahue, Anna Wolter, Pat Henry, Neal Trentham, and with our CNOC colleagues (E. Ellingson, H. Yee, R. Carlberg, R. Abraham) and others (N. Kaiser, Y. Mellier, B. Fort). We are grateful to all those (P. Henry, B. Tully, L. Kofman, J. Dalcanton, L. Cowie, M. Metzger, S. Miyazaki) who read and commented on early drafts of this paper, and to Doug Clowe, who helped with preliminary FOCAS analysis of some of the clusters. Finally, we appreciate the patience and generosity of Brent Tully who allowed us to "take an image or two'' during several of his observing runs. The UH CCD cameras were constructed using NSF Grant AST-9020680. This work also received partial financial support from NASA-STScI grant GO-05987.02-94A, NSF Grants AST-9119216 and AST-9500515, NASA Grants NAG5-2594, NAG5-2914, and ASI grants ARS-94-10 and ARS-96-13.