Cluster LensingCluster Lensing

Modeling, Physics & CosmologyModeling, Physics & Cosmology

Jean-Paul KNEIBLaboratoire d’Astrophysique de Marseille, France

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Outline

• Cluster Lens Modeling

• Recent results– Mass distribution - small to large scales

– Scaling relations

– Cosmology

– [Cosmic Telescope: Hi-z, SN]

• Prospects

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More than 2 decades ago: 1st arc in cluster

• 1987 the first giant luminous arc discovered• “Cluster are massive and dense enough to

produce strong lensing - they must be filled with dark matter”

• Every massive cluster is a lens !!!

Abell 370Abell 370CFHT - 1985CFHT - 1985 WFPC2- 1996WFPC2- 1996

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Lensing Back to Basics• Basics of lensing:

– Large mass over-densities locally deform the Space-Time

– A pure geometrical effect, no dependence with photon energy - depends on TOTAL MASS

• Lensing by (massive) clusters– Deflection of ~10-50 arcsec– strongly lens many background

sources => allow detailed mass reconstruction at different scales: cluster core, substructures, large scales

– ~1 SL cluster-lens per ~10 sq. deg: potentially ~2000 to study, Probably only ~200 identified today, nearly 20 with “a good” (SL) mass model

Ned Wright

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Halo Mass FunctionCluster mass function evolves strongly with redshift => cosmological probe (growth factor)

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2DSL+WL

1DWL

1DWL Stacking

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X-ray Luminosity

t~2Gyr t~2Gyr t~2Gyr

z=0 z=0.2 z=0.5 z~1

Massive X-ray selected Cluster

LoCuss

Hamilton-Morristalk

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• ~130 MACS clusters (z>0.3), HST, Subaru, Chandra, ground-based spectroscopy follow-up– Find many strong lensing clusters (>50% show SL)– Constrain cluster masses individually and in a statistical way with ultimately

possible cosmological implications

HST MACS survey

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MACSJ1149.5+2233MACSJ1149.5+2233

A

B

C

[OII] @ Z=1.48MACSJ1206.2-0847MACSJ1206.2-0847

Ebeling et al 2009

Smith et al 2009

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Optically Selected Strong lensing ClustersRCS-1 (Rz survey ~90 deg2), 5 arcs (Gladders et al 2003) found by visual inspection

CFHT-LS wide (150 deg2 provides a few arcs in clusters): Cabanac et al 2007

RCS-2 ~830 deg2 provide better stat a few tens

SDSS Altogether more than 200 clusters identified with bright arcs (Gladders et al 2009, Oguri et al 2009)

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Modeling:Mass Distribution

Measurement

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Mass Distribution Measurement

• How do we measure mass ?• Central mass profile ? => learn about DM and

baryon interactions• Large scale mass profile and substructures ?

=> structure formation paradigm, halo models• Case of mergers => probe nature of DM• Comparison of the distribution of the different

components => scaling relations, cluster thermodynamics

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SL Cluster Modeling and Errors Constraints:– Multiple images (position, redshift, flux, shape)– Single images with known redshift– Light/X-ray gas distributionModel parameterization– Need to include small scales: galaxy halos

(parametric form scaled with light)– Large scale: DM/X-ray gas (parametric form or

multi-scale grid)Model optimization – e.g. Bayesian approach (robust errors)– Not a unique solution: “most likely model and

errors”– Predict amplification value and errors => cluster as

telescopes

Jullo et al 2007, Jullo & Kneib 2009 LENSTOOL public software http://www.oamp.fr/cosmology/lenstool

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Where is the Matter in A2218?

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BAD FIT GOOD FIT

MATTER vs GAL. LIGHT MATTER vs. X-Ray Gas

Strong Lensing constraints in Abell 2218: Mass distribution proportional to the stellar mass produce a BAD FIT to the lensing dataRequire large scale mass distribution (cluster DM)Important difference between DM , Galaxy distribution and X-ray gas (different physics)But, scaling relation should exists

Eliasdottir et al. 2009

Mass scales with stellar mass

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Deep = Many

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Deep HST/ACS multi-band imaging of massive clusters provides MANY multiple images:A1689 ~40 systemsA1703 ~20 systemsStandard parametric modeling have the RMS image position fit proportional to number of constraints = model too rigid!

Need a change of paradigm in strong lensing mass modelingGrid approach: Jullo & Kneib 2009LensPerfect approach: Coe et al 2008

Limousin et al 2008. Richard et al 2009Limousin et al 2008. Richard et al 2009

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X KECK/LRIS

X VLT/FORS

X CFHT/MOS

X MAGELLAN

/LDSS2

X Littérature

• Mass models form different groups w. or w/o weak lensing• Massive spectroscopic surveys (2003-2006) • 41 multiple image systems, 24 with spectro-z with 1.1 < z < 4.9

Broadhurst et al 2005Halkola et al 2007Limousin, et al. 2007 Richard et al. 2007Frye et al 2007Leonard et al 2007Jullo & Kneib 2009 …

The most massive cluster: Abell 1689

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Multi-Scale Grid Based Modeling

More flexible ”multi-scale” model:• hexagonal/triangle padding- to match

the natural shape of clusters• Multi-scale: split triangles according to

a mass density threshold • Circular mass clump at each grid point:

– Truncated isothermal profile with a core– size of the mass clump depends on the

grid: r_core =grid-size– Truncation also depends on the grid:

r_cut/r_core = 3– one free parameter for each clump

• Add galaxy-scale mass clumps• MCMC optimized• Easy extension to WL regime

ACS field of A1689

Jullo & Kneib 2009Jullo & Kneib 2009

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Application to Abell 1689

Mass map similar to Limousin et al 2007 mean RMS = 0.22” RMS min = 0.09” max = 0.48” (sys6)

Mass distribution and S/N map (300,200,100,10)

Jullo & Kneib 2009Jullo & Kneib 2009

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LensPerfect - not yet perfect !

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•IDEA: Solve lensing equation perfectly using curl-free basis of function

•However for a multiple image system, there is an infinity of solution depending on the source position

•What is the most likely “perfect model” ???

•Perfect model only converge if an infinity of constraints …

Coe et al 2008, Coe 2009

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Mass Profile of Clusters (SL+Dynamics)

Sand, et al. 2007

•DM simulation predicts a universal profile; what is observed in the inner core?

•Combination of strong lensing (radial and tangential arcs) + dynamical estimates from the cD galaxies

•Some degeneracies, but indication of a flatter profile than canonical NFW: -0.5<beta<-1•“Flat” core found in other clusters (RCS0224, Cl0024)

•Possibly probe DM & Baryon coupling?

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Abell 383

MS2137

New detailed modeling

Kneib JENAM-09 19Log(radius)

Log

(she

ar)

HST/WFPC2 mosaic

SUBARU

CFHT

Mass Profile of Clusters (SL+WL)

Limousin, et al. 2007, Dahle et al 2009

•background source selection is critical to accurately measure WL

•Improved lensing constraints, revised concentration from c~15 to c~8

•Better agreement.•See also: Smith/Hoekstra talks

Abell 1689

« Bullet Cluster » unusually strong mergers

1E06571E0657

•Encounter of 2 massive clusters•Significant offset between X-ray gas and lensing mass peaks probably best evidence for « collision-less dark matter » put constraints on DM/baryon interactions

Clowe et al 2006,Clowe et al 2006,

Bradac et al 2006Bradac et al 2006

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Combining the Chandra data with lensing mass maps -> place an upper bound on the dark matter self-interaction cross section:

Baby bullet:σ/m < 4 cm2g−1 = 8

barn/GeV.Bullet cluster:σ/m < 0.7 cm2g−1 =

1.3barn/GeV (Randall et al.2008)

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Other « Baby Bullet» and Nature of DM

MACSJ0025-1222Bradac et al 2008

Physics:Cluster/Group Lensing

in the Field, Scaling Relations

Kneib JENAM-09 23WL mass calibration for X-ray clusters

23

Massey et al. 2007

Cluster/groups in COSMOS

~200 XMM cluster candidates:64 clusters: 0.5<z<1.0 50 clusters: z> 1(Finoguenov et al 2007, 2008)

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Photo-z concentration

X-ray clusters

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Photozz=0.8z=0.6z=0.4z=0.2

IAB<25

1.4M galaxies

X-raycontours

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• Weak Lensing in COSMOS not only allows tomography (Massey 3D map) but makes possible a direct measurement of mass of structures down to galaxy sizes

Clusters/Groups in COSMOS probed by WL

Leauthaud et al 2009

mas

s p

rofi

le

radius

0.4 keV 0.8 keV 1.6 keV

X-ray Luminosity vs Lensing Mass

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• M ~ L 0.6 over 3 decades in X-ray luminosity! (slope inconsistent with self-similar prediction)• But redshift evolution: consistent with self-similar model

Results: Lensing mass as a function of X-ray luminosity

Possibility to use other mass proxy like richness (used for SDSS measurement)

Leauthaud et al 2009

Cosmological World Model

Cosmography with SL clusters

Golse et al 2002, Soucail et al 2004Golse et al 2002, Soucail et al 2004

Abell 2218Abell 2218

•Lensing depends on cosmology via the angular distance. Probing different source planes, one probes different distances!=> Clusters with many (>>3) multiple image systems at different redshift can constrain cosmology

•Early work on A2218: with 4 multiple image systems at z=0.7, 1.03, 2.55, 5.56 favors Lambda-CDM• Need of deep imaging and deep spectroscopy …

Omega_matter

Om

ega_

lam

bd

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Cosmography with Abell 1689Mass model with 12 multiple image systems with

spectroscopic redshifts.

Optimizing cosmography (M , wX ) for a flat Universe

Jullo et al 2009Jullo et al 2009

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Cosmography with Abell 1689Mass model with 12 multiple image systems with

spectroscopic redshifts.

Optimizing cosmography (M , wX ) for a flat Universe

Jullo et al 2009Jullo et al 2009

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Combination with other cosmological probes (WMAP5, SDSS-BAO, SNLS) => mild improvement

Evidence for a non Lambda cosmology ??

More cluster cosmography constraints needed!Easier than Cosmic shear?

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Future Prospects• Lensing images better from space => true for cluster

lensing too (both SL and WL), multicolor very helpful• Mass reconstruction techniques are limited by

quality/quantity of data => results will improve with better, larger dataset … and faster computers!

• Slope of DM and substructure are measurable quantities => need to improve datasets

• Cluster cosmography is a promising new (geometrical) cosmological probe - Simple? Competitive?

• New serviced HST and JWST, as well as wide-field/spectroscopy ground-based 8-10m telescope are unique tools to conduct cluster lensing science.