6 Conclusion

Thanks to the deep multicolour subarcsecond images obtained with FORS1 and ISAAC, it was possible to carry out a weak-lensing analysis of the galaxy cluster MS 1008-1224 in considerable detail:

• We made mass maps using data from 4 different bands and two different algorithms. The very similar structures seen in all maps confirmed that the presciptions for PSF corrections and noise weighting were appropriate and the reconstruction algorithms worked well.

• The remarkable stability seen in the reconstructions meant that systematic errors, if any, were essentially due to the fixed positions and intrinsic ellipticities of the background lensed galaxies. So parametric bootstrap simulations using a realistic model for the mass and noise distributions (using the data itself) allowed us to quantify the effect of those factors. In particular, we carried out a large number of simulations to determine the positional stability of mass features.

• The above analysis helped us quantify the significance of the offset seen between the cD galaxy and the mass centroid. Our shear and depletion analyses and the X-ray image from Lewis et al. (1999) all suggest an offset of 10-20 arcsec ( 30-60  h^-1 kpc).

• The deep BVRIJK images were used to estimate the (photometric) redshifts of a representative sample of galaxies and determine the redshift distribution of the background/lensed population. This was used to scale the gravitational convergence ($\kappa$) into a mass value. We believe that this is the first time that redshifts have been used to determine this $\kappa$-to-mass scaling.

• We used the photometric redshifts to study the 3-Dim distribution of background galaxies and discovered a remarkable case of cluster-cluster lensing - another first. We identified a cluster at $z \sim 0.9$ which had been sheared and (presumably) amplified by MS 1008-1224 in the manner of the individual galaxies comprising it.

• Unfortunately, the contamination of the depletion curve by this lensed cluster partly compromised the use of the magnification bias effect to estimate the mass of the cluster independent of the weak shear analysis. This kind of clustering is an intrinsic limitation to the practical usefulness of the magnification bias which has already been emphasized by Fort et al. (1996) and Hoesktra et al. (1999).

• On a more optimistic note, MS 1008-1224 is a gravitational telescope facilitating by its amplification the study of a cluster of galaxies at $z \sim 1$. The amplification should have made more galaxies of this distant cluster observable than would have been possible otherwise. We have not dwelt on this point since it is beyond the scope of this work; a join multicolour and spectroscopic analysis of this cluster could be valuable.

• Weak-lensing technique only provides a lower limit to the lensing mass but comparison with (currently) plausible model profiles suggest that the underestimation is unlikely to be large for MS 1008-1224. On large scales, the mass inferred from weak lensing agrees with the X-ray estimate. In contrast, there is still a considerable amount of discrepancy on small scales. The clumpiness of the light distribution, the elongated shape, the X-ray emissivity, the double peak in the mass distribution and the offset between the cD galaxy and the mass centroid all indicate a dynamically unrelaxed cluster. We therefore believe that the X-ray gas is not in equilibrium in the innermost part of the cluster and this is the principal reason for the mass discrepancy which increases towards the centre.

• Further analysis of this cluster requires (i) infrared observations of the entire FORS1 field to determine the photometric redshifts of galaxies beyond 1 arcmin from the cluster center and hence a better estimate of the zero point of the depletion curve and (ii) HST images of the cluster center to model the innermost regions using strong-lensing features. The high resolution combined with photometric redshifts of arclets should make for a more accurate determination of the cluster center and the strong-lensing mass estimate.

Acknowledgements

We thank H. Hoesktra for providing his own updated version of the IMCAT software and for discussions on weak lensing. We thank also E. Bertin, T. Erben, N. Kaiser, R. Maoli, D. Pogosyan and P. Schneider for fruitful discussions. We acknowledge the helpful comments of an anonymous referee which considerably improved our presentation. We acknowledge efforts of the Science Verification Team of FORS1 and ISAAC at ESO for making available this excellent dataset to the ESO community.

The TERAPIX data center provided its computing facilities for the data reduction, the lensing analyses and the simulations. This work was supported the TMR network "Gravitational Lensing: New Constraints on Cosmology'' and the Distribution of Dark Matter'' of the EC under contract No. ERBFMRX-CT97-0172 and the Indo-French Centre for the Promotion of Advanced Research IFCPAR grant 1410-2.