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…………
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RE1 =4πσ 2
c 2DLS1DOS1
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RE2 =4πσ 2
c 2DLS2DOS2
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RE1RE2
= [DLS1DOS1
][DOS2DLS2
]
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Dij ≡ f (zi,z j ,ΩM ,Ωx,wx )
Obtained from data Solve for cosmological parameters
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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
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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
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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