## Constraining from weak lensing in clusters: the triplet statistics
^{1} DEMIRM, Observatoire de Paris, 61 Av. de l'Observatoire, 75014 Paris, France and URA 336 du CNRS^{2} Institut d'Astrophysique de Paris, 98 bis boulevard Arago, 75014 Paris, France
We present a new geometrical method, the On each background galaxy, a cluster induces a magnification which
depends on the local convergence and shear terms and on the
More precisely The calculation and the comparison of each source of statistical
noise is performed. The linear form of 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.
## Contents- 1. Introduction
- 2. The weak lensing equations
- 3. The triplet statistics
- 3.1. Construction of
- 3.2. Construction of
*G* - 3.3. The main cosmological term:
- 3.4. Noise on G
- 3.5. Resulting signal to noise ratio
- 3.6. The probability distribution
- 4. Analysis of systematics
- 4.1. Non symmetry of the term
- 4.2. Potential perturbation due to galaxy-galaxy lensing
- 4.2.1. The additive linear term
- 4.2.2. The multiplicative coupling term
- 4.3. Potential perturbation due to background lensing structures
- 4.3.1. The additive linear term
- 4.3.2. The multiplicative coupling term
- 4.3.3. Effect of a background cluster
- 4.4. Outcome
- 5. Optimization of the triplet statistics
- 6. Simulations and results
- 7. Conclusion
- Acknowledgements
- Appendices
- References
© European Southern Observatory (ESO) 2000 Online publication: December 8, 1999 |