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)

jij

iij zgdz

2

)(

Theory

Principles of Weak Lensing

Distortion matrix:

Convergence:

Shear:

Critical surface density:

221

crit

212221121

1 ;)(

lsol

oscrit DD

D

G

c

4

2

22

21

1

1

j

iij

Weak lensing regime: << 1 (linear approximation) Measure shear and solve for the projected mass

Measuring the Shear

Quadrupole moments: )()(2 xIxwxxxdQ jiij

Ellipticity:2211

122

2211

22111

2,

QQ

Q

QQ

QQ

12 Shear:

12

21

1

1

ij

ii P Relation:

Lensing by Clusters of Galaxies

Mellier & Fort; Seitz et al.

Shear Projected Mass

Status

Mellier et al. 2002

Mass-to-light ratio:<M/L> 400 h Mo/Lo

corresponding to:m 0.3in agreement withother 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

MS1007-1224Athreya et al. 2002

Lensing by GroupsHoekstra 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=0.130.07for CDM model

Galaxy-Galaxy Lensing

Lensing with SDSS: Fischer et al. 2000; McKay et al. 2001

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 ML in other bands M/L~100-300 in all bands

McKay et al. 2001

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

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 1997Bernardeau et al. 1997; Hu & Tegmark 1999

Deep Optical Images

William Herschel TelescopeLa Palma, Canaries

16’x8’R<25.530 (15) gals/sq. arcmin

Systematic Effects: PSF anisotropy

Correction Method

KSB Method: (Kaiser, Squires & Broadhurst 1995)

PSF Anisotropy:

**

' sm

smg

gg P

P

PSF Smear & Shear Calibration:gP 1)(

Other Methods: Kuijken (1999), Kaiser (1999), Rhodes, Refregier & Groth (2000), Refregier & Bacon (2001), Bernstein & Jarvis (2001)

Cosmic Shear Measurements

2()=<2

>Bacon, Refregier & Ellis 2000Bacon, Massey, Refregier, Ellis 2001Kaiser et al. 2000Maoli et al. 2000Rhodes, Refregier & Groth 2001Refregier, Rhodes & Groth 2002van Waerbeke et al. 2000van Waerbeke et al. 2001Wittman et al. 2000Hammerle et al. 2001*

Hoekstra et al. 2002 *

Brown et al. 2002 *

Hamana et al. 2002 * * not shown

Shear variance in circularcells:

Cosmological Implications

13.097.03.0

68.0

8

m

07.000.13.0

60.0

8

m

Shear Variance: (CDM)8.07.02.1

8 mm z

WHT+ Keck measurement:

Clusters: Pierpaoli et al. 2001

Clusters: Seljak 2001

06.075.03.0

44.0

8

m

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. 2002

Hamana et al. 2002

Dark Clumps

Wittman et al. 2002: Discoveryand tomography of a z=0.68 cluster

Unidentified “dark clumps”:Erben et al. 2000; Umetsu & Futamase 2000;Miralles et al. 2002

Mass-Selected ClustersMiyazaki 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

Weak Lensing Power Spectrum

CDM

CDM(linear)

OCDM

SNAP WF survey [200 deg2; 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 tonon-linear evolution ofstructures

Mapping the Dark Matter

CDM0.5x0.5 degJain et al. 1998

HST TreasurySurvey:with ACS/HSTwide: 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