constraining cosmography with cluster lenses jean-paul kneib laboratoire d’astrophysique de...

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


Historical Perspective

• 1986/1987: discovery of the giant luminous Arcs in Cl2244 and Abell 370

1987: CFHT1987: CFHT 1996: WFPC21996: WFPC2


Lensing Theory

The Context:


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


Lensing Equations

Notations:

cosmology


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:


Lensing Equations

Lens Mapping:

: lensing potential

Link with catastrophe theory Purely geometrical: Achromatic effect

Lens Efficiency


Redshift and Cosmology

Lens Efficiency:

For a fixed lens redshift, the lens efficiency increase with source redshift

Weak cosmology dependence


Lensing Equations

Lens Mapping distortion (first order):

In polar coordinates:


Lensing EquationsAmplification Matrix:

: convergence

: shear vector

Reduced shear:


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)


Lensing Theory

Multiple image configurations for a non-singular elliptical mass distribution

Cusp arc

Fold arcEinstein cross

Radial arc

Single imageSource


Strong LensingLensing equation can have multiple solution:

Finding source is easy!

Finding the images need solving a 2D equation (ray tracing)


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)


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



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



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



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)


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)


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)


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


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 :


Best strong lensing data:Best strong lensing data: HubbleHubble (color) images (color) images

Abell 2218 at z=0.175


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


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


Cosmography with clusters lenses

Lensing efficiency:

Lens equation:


Cosmography with clusters lensesSingle multiple image system: degeneracy between the mass and the lens efficiency E:


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:


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


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)


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


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


A potentially interesting new cluster

Cl0152-05(z=0.83)

8 multiple images identified

Only one with spectroscopicredshift


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)


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)

constraining cosmography with cluster lenses jean-paul kneib laboratoire d’astrophysique de...

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