Weak Lensing

1. Weak Lensing Alexandre Refregier (CEA/Saclay) Collaborators: Richard Massey (Cambridge), Tzu-Ching Chang (Columbia), David Bacon (Edinburgh), Jason Rhodes (GSFC), Richard Ellis (Caltech) Reviews: Bartelmann & Schneider 2000; Mellier et al. 2002; Hoekstra et al. 2002; Wittman 2002 Santiago - October 2002

2. Distortion Matrix:  Direct measure of the distribution of mass in the universe, as opposed to the distribution of light, as in other methods (eg. Galaxy surveys) Weak Gravitational Lensing Theory

3. Principles of Weak Lensing Distortion matrix: Convergence: Shear: Critical surface density: Weak lensing regime:  << 1 (linear approximation)  Measure shear  and solve for the projected mass 

4. Measuring the Shear Quadrupole moments: Ellipticity: Shear: Relation:

5. Lensing by Clusters of Galaxies Shear  Projected Mass  Mellier & Fort; Seitz et al.

6. Status Mass-to-light ratio: <M/L>  400 h Mo/Lo corresponding to: m0.3 in agreement with other methods Mellier et al. 2002

7. Prospects for Clusters • Oustanding questions: • Combine weak lensing with X-rays: •  compare lensing and X-ray masses •  measurement of the M-T relation • Construction of a mass-selected cluster catalogue • Measurement of the density profiles of clusters  stacking MS1007-1224 Athreya et al. 2002

8. Lensing by Groups Hoekstra et al. 2000: 50 galaxy groups from CNOC2 survey with v=50-400 km/s, <z>=0.33 Mass-to-light ratio: <M/L>  191 h Mo/Lo corresponding to: m=0.130.07 for CDM model

9. Galaxy-Galaxy Lensing Effectively stack a large number of foreground galaxies and measure the average tangential shear using background galaxies. Lensing with SDSS: Fischer et al. 2000; McKay et al. 2001  Galaxies (esp. ellipticals) are members of groups and clusters

10. Mass and light in Galaxies McKay et al. 2001 Fit Mass-Luminosity relation: M= a L (within 260 kpc/h)  Poor M-L relation in u-band  ML in other bands  M/L~100-300 in all bands

11. Lensing by Superclusters Abell 901/902 Supercluster • Gray et al. 2001 • (see also Kaiser et al. 1998) • Evidence for a filament • M/L varies from cluster to cluster • Cross-correlation: reveals non-linear or stochastic biasing •  Careful when deriving mfrom M/L

12. Cosmic Shear From the statistics of the shear field, weak lensing provides: • Mapping of the distribution of Dark Matter on various scales • Measurement ofcosmological parameters, breaking degeneracies present in other methods (SNe, CMB) • Measurement of the evolution of structures • Test of gravitational instabilityparadigm • Test of General Relativity in the weak field regime Kaiser 1992, 1998; Jain & Seljak 1997 Bernardeau et al. 1997; Hu & Tegmark 1999 Jain, Seljak & White 1997, 1x1 deg

13. Deep Optical Images William Herschel Telescope La Palma, Canaries 16’x8’ R<25.5 30 (15) gals/sq. arcmin

14. Systematic Effects: PSF anisotropy

15. Correction Method KSB Method: (Kaiser, Squires & Broadhurst 1995) PSF Anisotropy: PSF Smear & Shear Calibration: Other Methods:Kuijken (1999), Kaiser (1999), Rhodes, Refregier & Groth (2000), Refregier & Bacon (2001), Bernstein & Jarvis (2001)

16. Cosmic Shear Measurements Shear variance in circular cells: 2()=<2>  Bacon, Refregier & Ellis 2000 Bacon, Massey, Refregier, Ellis 2001 Kaiser et al. 2000 Maoli et al. 2000 Rhodes, Refregier & Groth 2001 Refregier, Rhodes & Groth 2002 van Waerbeke et al. 2000 van Waerbeke et al. 2001 Wittman et al. 2000 Hammerle et al. 2001* Hoekstra et al. 2002 * Brown et al. 2002 * Hamana et al. 2002 * * not shown

17. Cosmological Implications Shear Variance: (CDM) WHT+ Keck measurement: Clusters: Pierpaoli et al. 2001 Clusters: Seljak 2001 Bacon et al. 2002

18. Normalisation of the Power Spectrum Brown et al. 2002  Moderate disagreement between the previous and most recent cosmic shear measurements  This could be due to residual systematics  Better agreement with new cluster abundance normalisation  Otherwise, may require revision of the CDM paradigm Hamana et al. 2002

19. Dark Clumps Wittman et al. 2002:Discovery and tomography of a z=0.68 cluster Unidentified “dark clumps”: Erben et al. 2000; Umetsu & Futamase 2000; Miralles et al. 2002

20. Mass-Selected Clusters Miyazaki et al. 2002: 2.1 deg2 survey with Subaru • complex relation between mass and light • bright cluster counts in agreement with CDM models • discovery of new clusters

21. Weak Lensing Power Spectrum OCDM Future surveys: CFHT, Keck, WHT, Subaru, ACS/HST Future Instruments: Megacam, VST, VISTA, LSST, WHFRI, SNAP, GEST  Measure cosmological parameters (8, m, , , w, etc)  very sensitive to non-linear evolution of structures CDM CDM (linear) SNAP WF survey [200 deg2; 80 g arcmin-2; HST image quality]

22. Mapping the Dark Matter HST Treasury Survey: with ACS/HST wide: 2x35’x35’ deep: 4x15’x15’ CDM 0.5x0.5 deg Jain et al. 1998

23. Conclusions • Weak lensing is based on clean physics and provides a direct measure of the distribution of mass in the universe • Weak lensing now provides precise measurements on a wide range of scales: galaxies, groups, clusters, superclusters, large-scale structure • Upcoming surveys with wide field cameras offer exciting prospects for weak lensing