weak lensing
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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,
Q
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
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