Astron. Astrophys. 363, 401-414 (2000)

7. Conclusions

We have studied the weak lensing mass distribution of the cluster MS1008 using multicolor imaging data obtained during the Science Verification of FORS1 on the VLT. The depth, angular resolution, and image quality across the entire field of view make these images a rare and ideal dataset for weak lensing analysis. In addition, the information on radial velocities of a large set of cluster galaxies provided by the CNOC survey allows the mass of this cluster to be derived with dynamical methods and compared with that reconstructed from the weak lensing. These combined datasets allowed us to conduct a detailed study of the systematic effects involved in cluster mass estimates.

We have found PSF distortions of FORS1 to be moderate and hence easily removed with a low order polynomial fit. The B through I multicolor information, as well as the redshift information from the CNOC catalog, have allowed us to efficiently separate the background galaxies from the cluster and foreground populations. Approximately 8000 objects have been detected, corresponding to . Further selection lead to approximatively 1700 background galaxies with high signal-to-noise ratio which have been used for the determination of lensing shear field. We have detected a weak lensing signal out to . The projected mass within is measured in the range in the four filters, with typical statistical errors (deriving from uncertainties in galaxy ellipticities) of 5%.

We have discussed the impact of systematics in the weak lensing reconstruction of the mass distribution in physical units, which can be summarized as follows. The removal of the mass-sheet degeneracy is inevitably model-dependent, inducing mass variations of at . [Note that the estimate of this error is difficult and somewhat arbitrary since the error clearly depend on the "range" of possible models allowed. As a result, the estimate of the total error, given below, is also bound to be inaccurate. We stress, however, that a similar problem exists for X-ray or virial mass estimate (cf., e.g., the different predictions using King-like or NFW profiles if Fig. 13).] By polluting the background galaxy population with a significant fraction of cluster galaxies, the total mass is biased low by . However, different selections of background galaxies, as well as edge effects due to masked portions of the images, do affect the morphology of the shear maps. We have not found any evidence for a substructure of the cluster core; this in part is due to lack of resolution in the mass reconstruction, set by the smoothing scale used. However, we have found the central region of the cluster to be elongated NS, with some evidence of a displacement of the projected mass peak respect to the cD galaxy, similarly to the X-ray emission. Cosmic variance is expected to affect the assumed redshift distribution of the background field galaxies, and hence the derived cluster mass. From a comparison between the Hubble Deep Field North and South, cosmic variance would introduce a systematic error of approximatively in the mass. This can also be taken as a rough estimate of the error due to cosmic variance. Note also the main contribution to this error is from large scale structures rather than from Poisson noise in the HDF-N and in our field. In other words, a simple error estimate which assumes that galaxies are uncorrelated would lead to an underestimate of the error. Altogether, the cluster light distribution traces the mass distribution remarkably well. We have measured a mass-to-light ratio of at radii Mpc.

We have also compared the weak lensing mass profile with that derived from a virial analysis of the CNOC redshift data, as well as with the X-ray mass. The mass derived from X-ray observations (Lewis et al. 1999) is found in excellent agreement with our weak lensing determination at . Different approaches to estimate the cluster mass at the virialization scale produce very similar results. At scales Mpc, lensing and virial mass determinations can be compared. The virial mass reconstruction at these small radii critically depends on the assumed density profile. Using a King-like profile describing the galaxy distribution of local clusters (G98; cf. also Eq. (15)), we have obtained a mass which is more than away from the X-ray and weak-lensing mass. Assuming instead a NFW profile, as fitted by Carlberg et al. (1997) to CNOC clusters, a much better agreement is obtained over the entire overlapping region. Note that the discrepancy at small radii () between lensing and virial estimate can be explained by recalling that the lensing determination is affected by a Gaussian smoothing of , as well as a departure from the weak lensing approximation. The former effect leads to underestimate the mass in the core, while the latter will generally bias the central mass high. Both effects clearly vanish at large radii. In addition, we notice that the weak lensing data alone cannot discriminate between different mass profiles (e.g. NFW versus isothermal model).

This analysis shows that the combination of depth and good imaging quality provided by VLT/FORS allows us to obtain high mass maps via optimized weak lensing reconstruction methods. On the other hand, these data have the virtue of revealing important systematic errors in weak lensing analyses. We find that the mass-sheet degeneracy dominates the budget of systematic errors and ultimately makes mass measurements via weak lensing model dependent.

The results obtained here are, at a first look, in good agreement with the mass reconstruction performed by Athreya et al. (2000). However, a detailed analysis of their study reveals that a different recipe to remove the mass-sheet degeneracy was used. Specifically, they set to zero the mass at large radii (-). Had they used our (model-dependent) method to break the mass-sheet degeneracy, their estimate would have been a factor of two higher. Therefore, there is a discrepancy of the same factor between the two analysis which, at present, we are unable to explain.

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
helpdesk.link@springer.de