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

Weak Gravitational Lensing 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) Theory

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 

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

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

Status Mellier et al Mass-to-light ratio:  400 h M o /L o corresponding to:  m  0.3 in agreement with other methods

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 MS Athreya et al. 2002

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

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

Mass and light in Galaxies 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~ in all bands McKay et al. 2001

Gray et al (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  m from M/L Lensing by Superclusters Abell 901/902 Supercluster

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

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

Systematic Effects: PSF anisotropy

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)

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

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

Normalisation of the Power Spectrum  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 Brown et al Hamana et al. 2002

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

Mass-Selected Clusters Miyazaki et al. 2002: 2.1 deg 2 survey with Subaru complex relation between mass and light bright cluster counts in agreement with CDM models discovery of new clusters

Weak Lensing Power Spectrum  CDM (linear) OCDM SNAP WF survey [200 deg 2 ; 80 g arcmin -2 ; HST image quality] 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

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

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