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Constraining Cosmography with Cluster Lenses
Jean-Paul Kneib
Laboratoire d’Astrophysique de Marseille
19 Sept. 2005 JP KNEIB -- Dark Universe 2
PLAN
• Quick introduction of cluster strong lensing
• How to find multiple images ?• How do we constrain cosmology ?• Future prospects
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Historical Perspective
• 1986/1987: discovery of the giant luminous Arcs in Cl2244 and Abell 370
1987: CFHT1987: CFHT 1996: WFPC21996: WFPC2
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Lensing Theory
The Context:
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Cluster Cluster LensesLenses
Most massive clusters Einstein radius: 10-45”
Strong Lensing in the core,Weak lensing on large scale
Ned Wrigth, UCLA
Possible uses: Measure total mass distribution of cluster Study magnified distant sources Constrain Cosmography
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Lensing Equations
Notations:
cosmology
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Cluster Lens equations
Assumptions:
• Cosmological principle (homogeneous and isotropic)metric of the Universe (cosmography)
• Thin lens approximation
• Potential of the lens is slowly varying
• Small deflection:
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Lensing Equations
Lens Mapping:
: lensing potential
Link with catastrophe theory Purely geometrical: Achromatic effect
Lens Efficiency
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Redshift and Cosmology
Lens Efficiency:
For a fixed lens redshift, the lens efficiency increase with source redshift
Weak cosmology dependence
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Lensing Equations
Lens Mapping distortion (first order):
In polar coordinates:
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Lensing EquationsAmplification Matrix:
: convergence
: shear vector
Reduced shear:
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Lensing Equations
Definition: Critical linesLocus of the image plane where the determinant of the
(inverse) magnification matrix is zero:
Critical lines are closed curves and non over-lapping.
In general: 2 types of critical lines:- tangential (external)- radial (internal)
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Lensing Theory
Multiple image configurations for a non-singular elliptical mass distribution
Cusp arc
Fold arcEinstein cross
Radial arc
Single imageSource
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Strong LensingLensing equation can have multiple solution:
Finding source is easy!
Finding the images need solving a 2D equation (ray tracing)
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Lens Modeling with Multiple ImagesLens Modeling with Multiple Images• One system with N images:- # of constraints: 2N, 3N (image position+flux)
- # of unknown: 2, 3 (source position+flux)
- # of free parameter: 2(N-1), 3(N-1)
Double: 2, 3 Triple: 4, 6 Quad: 6, 9
systems of N images:- # of free parameters: 2(N-1), 3(N-1)- need to substract number of unknown redshift !!
30 triples: <120, <180 [A1689 with ACS => deep JWST observations] [A1689 with ACS => deep JWST observations]
parametric models favored Introduce other constraints:
critical line location and/or external constraints from
X-ray observations or velocities (of stars in central galaxy)
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How to identify multiple images ?How to identify multiple images ?
Extreme distortion: Giant arcs are the merging of 2 or 3 (or possibly more) multiple images
Giant arc in Cl2244-04, z=2.24,Septuple image
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How to identify multiple images ?How to identify multiple images ?
Morphology: Change of parity across a critical line.
Note: The lensing amplification is a gain in the angular size of the sources. Allow to resolve distant sources and study their size and morphologies.
Lensed pair in AC114, z=1.86
Critical Line
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How to identify multiple images ?How to identify multiple images ?
Example of a triple ERO system at z~1.6 (Smith et al 2002) lensed by Abell 68
Interest of magnification is to allow to resolved the morphology of these systems: showing the presence of disks in particular, thus understanding the Nature of ERO.
Extreme similar colors:
Abell 68: ERO triple image at z~1.6
R+K Color image
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How to identify multiple images ?How to identify multiple images ?
Color and Morphology:
Lens model can help for the identification when different solution are possible
Quintuple arc (z=1.67)inCl0024+1654 (z=0.39)
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Strong Galaxy-Strong Galaxy-Galaxy Lensing in Galaxy Lensing in
ClusterCluster
Cluster Galaxies are breaking arcs into smaller ones, adding new images of the lensed galaxy.
Abell 2218, arc at z=0.702, with 8 imagesidentified (the arc is the merging of 2 images)
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Strong Lensing modeling strategyCluster are complex systems with (at least) 3
different mass components: galaxies (stars and their DM halo), X-ray gas and Dark Matter
Small number of lensing constraints, better suited for parametric approach: e.g. Kneib et al 1996 (A2218), see also Tyson et al 1998 (Cl0024)
Non-parametric methods require either:– Prior on the mass distribution from the light
(Abdelsalam et al 1998)– (Rare) systems with many multiple images (Diego
et al 2005)
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Parametric maximum Likelihood method
• large scale cluster component+galaxy halo components (stars+DM):
• need to scale the galaxy halo components; for example for a PIEMD mass distribution:
• Hence:ConstantM/L
FP scaling
Kneib et al 1996
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Maximum Likelihood expressionsLikelihood of the image positions can be computed:
- in the source plane [easier no inversion needed]
- or in the image plane [better, because real error estimate possible]
Source plane:
Image plane:
Possible guess for :
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Best strong lensing data:Best strong lensing data: HubbleHubble (color) images (color) images
Abell 2218 at z=0.175
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Cluster Lens: Mass Reconstruction•Parameterized mass distribution, involving various multiple image system•Need to include galaxy scale mass component using scaling relations
Kneib et al 1996, Golse et al 2002
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Multiple Images and Cosmology
• Lensing depends on cosmology via the angular diameter distance
• system with many multiple image systems at different redshift can constrain cosmology
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Cosmography with clusters lenses
Lensing efficiency:
Lens equation:
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Cosmography with clusters lensesSingle multiple image system: degeneracy between the mass and the lens efficiency E:
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Cosmography with clusters lensesTWO multiple image systems at different redshift: one get rid of the mass normalisation,
but likely degeneracy between the mass profile and the lens efficiency E:
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Cosmography with clusters lensesTHREE or more multiple image systems at different redshift: should get rid of the mass profile degeneracy with the lens efficiency E.Better constraints if the redshifts span the different possible value of the
lens efficiency
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Cosmography with clusters lenses
Simulation with THREE multiple image systems at different redshift
Shape of contours may tell us about the Goodness of fit (case of a missing clump)
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Results from A2218 Results from A2218 & Prospects& Prospects
• 4 multiple image systems at z=0.7, 1.03, 2.55, 5.56 in Abell 2218• more potential as ~5 other multiples with no redshift yet• add more external constraints like velocity dispersion of galaxies• prospects more clusters available observed with deep ACS data, need redshift determinations!
Soucail, Kneib, Golse, 2004
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Critical requirements for cosmography with Cluster Lenses
• Many multiple images with Spectroscopic redshift (=>interest of IFS)
• Images with different redshifts Examples: A2218 (z=0.18): ~10 systems,
5 with z, A1689 (z=0.18) ~30 systems, a few with z, A370 (z=0.37): ~5 systems, 2 with z
New: Cl0152-05 (z=0.83): 8 systems, 1 with z
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A potentially interesting new cluster
Cl0152-05(z=0.83)
8 multiple images identified
Only one with spectroscopicredshift
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Noise in Lensing Cosmography• Distribution of mass along the line of sight needs proper modeling of all lensing planes
( with complete redshift survey) Needs different line of sight • Limitation from the (parametric) mass
distribution models: Include weak shear constraints and external
constraints like dynamical estimate or X-ray need a robust approach to find the best
models (MCMC approach)
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Conclusion
A potential new method for cosmography Need further tests of its usefulness (realistic
simulations + real clusters) Study in every possible details, a number of
clusters to check consistency. SNAP/DUNE will allow discoveries of many
systems & JWST will study them in details (imaging and spectroscopy)
END