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Constraining from weak lensing in clusters: the triplet statistics
L. Gautret 1,
B. Fort 2 and
Y. Mellier 1,2
Received 22 December 1998 / Accepted 18 October 1999
We present a new geometrical method, the triplet statistics , which uses weak gravitational lensing effects around clusters to constrain the cosmological parameters and .
On each background galaxy, a cluster induces a magnification which depends on the local convergence and shear terms and on the cosmological parameters (, ) through the angular distance ratio . To disentangle the effects of these three quantities, we compare the ellipticities of each triplet of galaxies located at about the same apparent position in the lens plane, but having different redshifts. The simultaneous knowledge of ellipticities and redshifts of each triplet enable to build a purely geometrical estimator (hereafter the -estimator) independently of the lens potential.
More precisely G has the simple form of the determinant of a 3-3 matrix built with the triplet values of and observed ellipticities. When G is averaged on many triplets of galaxies, it provides a global function of (, ) which converges to zero for the true values of the cosmological parameters.
The calculation and the comparison of each source of statistical noise is performed. The linear form of G regarding the measured ellipticity of each galaxy implies that the different noises on G decrease as , where N is the total number of observed distorted galaxies.
The possible systematics are analyzed with a multi-screen lensing model in order to estimate the effect of perturbative potentials on galaxy triplets. Improvements are then proposed to minimize these systematics and to optimize the statistical signal to noise ratio.
Finally, simulations are performed with realistic geometry and convergence for the lensing clusters and a redshift distribution for galaxies similar to the observed ones. They lead to the encouraging result that a significant constraint on (, ) can be reached: in the case or in the case (at a 1 confidence level). These constraints would be obtained from the observations of nearly 100 clusters, using multicolor imaging in order to get photometric redshifts of triplets. This corresponds to about 20 nights of VLT observations. The method looks even more promising with the NGST, in particular if it was used jointly with the supernovae search which provides orthogonal constraints.
Key words: galaxies: clusters: general cosmology: observations cosmology: dark matter cosmology: gravitational lensing
Send offprint requests to: Yannick Mellier (firstname.lastname@example.org)
Online publication: December 8, 1999