Cluster Lensing Modeling, Physics & Cosmology Jean-Paul KNEIB Laboratoire d’Astrophysique de Marseille, France

Kneib JENAM-092 Outline Cluster Lens Modeling Recent results –Mass distribution - small to large scales –Scaling relations –Cosmology –[Cosmic Telescope: Hi-z, SN] Prospects

Kneib JENAM-093 More than 2 decades ago: 1 st 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 370 CFHT WFPC

Kneib JENAM-094 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

Kneib JENAM-095 Halo Mass Function Cluster mass function evolves strongly with redshift => cosmological probe (growth factor) 2D SL+WL 1D WL 1D WL Stacking

Kneib JENAM-096 X-ray Luminosity  t~2Gyr z=0z=0.2z=0.5z~1 Massive X-ray selected Cluster LoCuss Hamilton-Morris talk

Kneib JENAM-097 ~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 surveyMACSJ A B C Z=1.48 MACSJ Ebeling et al 2009 Smith et al 2009

Kneib JENAM-098 Optically Selected Strong lensing Clusters RCS-1 (Rz survey ~90 deg 2 ), 5 arcs (Gladders et al 2003) found by visual inspection CFHT-LS wide (150 deg 2 provides a few arcs in clusters): Cabanac et al 2007 RCS-2 ~830 deg 2 provide better stat a few tens SDSS Altogether more than 200 clusters identified with bright arcs (Gladders et al 2009, Oguri et al 2009)

Kneib JENAM-099 Modeling: Mass Distribution Measurement

Kneib JENAM-0910 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

Kneib JENAM-0911 SL Cluster Modeling and Errors Constraints: –Multiple images (position, redshift, flux, shape) –Single images with known redshift –Light/X-ray gas distribution Model 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

Kneib JENAM-0912 Where is the Matter in A2218? BAD FITGOOD FIT MATTER vs GAL. LIGHTMATTER vs. X-Ray Gas Strong Lensing constraints in Abell 2218:  Mass distribution proportional to the stellar mass produce a BAD FIT to the lensing data  Require 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 Mass scales with stellar mass

Kneib JENAM-0913 Deep = Many Deep HST/ACS multi-band imaging of massive clusters provides MANY multiple images: A1689 ~40 systems A1703 ~20 systems Standard 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 modeling  Grid approach: Jullo & Kneib 2009  LensPerfect approach: Coe et al 2008 Limousin et al Richard et al 2009

Kneib JENAM-0914 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 ( ) 41 multiple image systems, 24 with spectro-z with 1.1 < z < 4.9 Broadhurst et al 2005 Halkola et al 2007 Limousin, et al Richard et al Frye et al 2007 Leonard et al 2007 Jullo & Kneib 2009 … The most massive cluster: Abell 1689

Kneib JENAM-0915 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 2009

Kneib JENAM-0916 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 2009

Kneib JENAM-0917 LensPerfect - not yet perfect ! 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

Kneib JENAM-0918 Mass Profile of Clusters (SL+Dynamics) Sand, et al 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? Abell 383 MS2137 New detailed modeling

Kneib JENAM-0919 Log(radius) Log(shear) 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 mergers1E0657 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, Bradac et al 2006 Bradac et al 2006

Kneib JENAM-0921 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) Other « Baby Bullet» and Nature of DM MACSJ Bradac et al 2008

Physics: Cluster/Group Lensing in the Field, Scaling Relations

Kneib JENAM-0923 WL mass calibration for X-ray clusters 23 Massey et al Cluster/groups in COSMOS ~200 XMM cluster candidates: 64 clusters: 0.5<z< clusters: z> 1 (Finoguenov et al 2007, 2008) Photo-z concentration X-ray clusters

Kneib JENAM-0924 Photoz z=0.8 z=0.6 z=0.4 z=0.2 I AB <25 1.4M galaxies X-ray contours

Kneib JENAM-0925 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 mass profile radius 0.4 keV0.8 keV1.6 keV

X-ray Luminosity vs Lensing Mass 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 2004 Abell 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 Omega_lambda

Kneib JENAM-0929 Cosmography with Abell 1689 Mass model with 12 multiple image systems with spectroscopic redshifts. Optimizing cosmography (  M, w X ) for a flat Universe Jullo et al 2009

Kneib JENAM-0930 Cosmography with Abell 1689 Mass model with 12 multiple image systems with spectroscopic redshifts. Optimizing cosmography (  M, w X ) for a flat Universe Jullo et al 2009 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?

Kneib JENAM-0931 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.