Constraining Dark Energy with Cluster Strong Lensing

Priyamvada NatarajanYale University

Collaborators: Eric Jullo (JPL), Jean-Paul Kneib (OAMP), Anson D’Aloiso*(Yale), Marceau Limousin (Toulouse), Johann Richard (DARK), Carlo Schimd (OAMP)

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

Einstein radii at multiple source redshiftsRatio 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 zsource!

How does this work?

ISOTHERMAL SPHERE LENS lens at z = zL; sources at zS1 & zS2

• EXTENDING TO MORE COMPLICATED MASS PROFILES AND MORE MULTIPLY IMAGED SOURCES…………

€

RE1 =4πσ 2

c 2DLS1DOS1

€

RE2 =4πσ 2

c 2DLS2DOS2

€

RE1RE2

= [DLS1DOS1

][DOS2DLS2

]

€

Dij ≡ f (zi,z j ,ΩM ,Ωx,wx )

Obtained from data Solve for cosmological parameters

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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

Strong lensingmultiple image geometries for an elliptical lens

Source plane caustics

Image planecritical curves

Multiple image families and sensitivity to dark energy

notation denotes the position of the ith 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 themass distribution

Mass profile of Abell 1689

First results for A1689

Limousin+ 07

Degeneracies….

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 galaxiesBayesian optimization: 32 constraints, 21 free parameters;RMS = 0.6 arcsec; 28 multiple images from 12 sources with spec z, flat Universe prior

€

0.1≤ ΩM ≤ 0.58;−1.57 ≤ wX ≤ −0.85

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

Contribution of structure behind the lens plane

D’Aloisio & PN 10

KEY SYSTEMATICSL.O.S. SUBSTRUCTURE IN LENS PLANE & ALONG L.O.SScaling Relations (relation between mass & light) Correlated LOS (infalling subclusters, filaments)Uncorrelated LOS (primary contribution to the errors)

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

10 clusters, 20 families!Flat prior, input w = -1; evolving

wa

€

wx = w0 + waz

(1+ z)

Chevallier, Polarski & Linder 01

Current constraints including CSL

Combining X-ray clusters, WMAP5, strong lensing competitive with WMAP5 + SNe + BAO

Jullo, Kneib, PN+ 10

The SDSS Giant-Arc Survey & MCT Clusters….

Hennawi+ 07, 08; Oguri+ 09; Gladders+ 10; Postman+

Parameter degeneracies

For each clump: ellipticity, core radius, clump vel disp, Omegam

wx