1. Constraining Dark Energy with Cluster Strong Lensing Priyamvada Natarajan Yale University Collaborators: Eric Jullo (JPL), Jean-Paul Kneib (OAMP), Anson D’Aloiso*(Yale), Marceau Limousin (Toulouse), Johann Richard (DARK), Carlo Schimd (OAMP)

2. HST’s high resolution Post COSTAR, Hubble has provided a unique view of multiply imaged galaxies: better identification, fainter images, morphologies 1996 HST Cl2244 1986 CFHT

3. Einstein radii at multiple source redshifts Ratio of the position of multiple images,depends on mass distribution and cosmological parameters Ratio of the position of multiple images,depends on mass distribution and cosmological parameters Allows constraining dark energy out to z source !

4. How does this work? ISOTHERMAL SPHERE LENS lens at z = z L ; sources at z S1 & z S2 EXTENDING TO MORE COMPLICATED MASS PROFILES AND MORE MULTIPLY IMAGED SOURCES………… Obtained from data Solve for cosmological parameters

5. Broadhurst+ 05, Benitez+ 06; Halkola+ 06; Limousin, PN+ 07; Jullo+ 2010 (Science) 34 multiply imaged systems, 24 with measured redshifts Cluster arcs and dark energy: Abell 1689

6. Strong lensing multiple image geometries for an elliptical lens Source plane caustics Image plane critical curves

7. Multiple image families and sensitivity to dark energy notation denotes the position of the i th image of family f For multiple images of the same source Taking the ratio of 2 distinct families of multiple images Gilmore & PN 08; D’Aloisio & PN 10 Dependence on the mass distribution

8. Mass profile of Abell 1689

9. First results for A1689 Limousin+ 07

10. Degeneracies….

11. First results for A1689 D’Aloisio & PN 09; Jullo & Kneib 09: Jullo+ 10 (Science, August 2010, 329, 924) Mass model with 3 PIEMD potentials; 58 cluster galaxies Bayesian optimization: 32 constraints, 21 free parameters; RMS = 0.6 arcsec; 28 multiple images from 12 sources with spec z, flat Universe prior

12. Requirements for cluster strong lensing Need complement of ground based spectroscopy Mass modeling positional accuracy Need spectroscopic redshifts for all sources (no photo-z’s) Structure along the line of sight behind the lens plane (environments of lenses needs to be modeled Momcheva et al. 06, Oguri, Keeton& Dalal 05) structure behind 0024 perturbations in the positions of multiple images Area under caustic likely to produce multiple images

13. Contribution of structure behind the lens plane D’Aloisio & PN 10 KEY SYSTEMATICS L.O.S. SUBSTRUCTURE IN LENS PLANE & ALONG L.O.S Scaling Relations (relation between mass & light) Correlated LOS (infalling subclusters, filaments) Uncorrelated LOS (primary contribution to the errors)

14. BIASES: choice of density profile, bimodality? Not particularly sensitive to the inner slope/outer slope of the density profile No bias from choice of profile NFW vs. PIEMD or bi-modality

15. 10 clusters, 20 families! Flat prior, input w = -1; evolving w a Chevallier, Polarski & Linder 01

16. Current constraints including CSL Combining X-ray clusters, WMAP5, strong lensing competitive with WMAP5 + SNe + BAO Jullo, Kneib, PN+ 10

17. The SDSS Giant-Arc Survey & MCT Clusters…. Hennawi+ 07, 08; Oguri+ 09; Gladders+ 10; Postman+

18. Parameter degeneracies For each clump: ellipticity, core radius, clump vel disp, Omega m wxwx