Constraining Cosmography with Cluster Lenses

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Constraining Cosmography with Cluster Lenses

• Jean-Paul Kneib
• Laboratoire dAstrophysique de Marseille

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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 CFHT
1996 WFPC2
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Lensing Theory

• The Context

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Cluster Lenses
Most massive clusters Einstein radius 10-45
Strong Lensing in the core, Weak lensing on large
scale

• Possible uses
• Measure total mass distribution of cluster
• Study magnified distant sources
• Constrain Cosmography

Ned Wrigth, UCLA
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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 Equations

• Amplification Matrix
• ? convergence
• ???????? shear vector
• Reduced shear

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Lensing Equations

• Definition Critical lines
• Locus 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
Single image
Source

• Multiple image configurations for a non-singular
  elliptical mass distribution

Radial arc
Cusp arc
Fold arc
Einstein cross
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Strong Lensing

• Lensing 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 Images

• One system with N images
• - of constraints 2N, 3N (image positionflux)
• - of unknown 2, 3 (source positionflux)
• - 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 lt120, lt180 A1689 with ACS gt 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 ?
Extreme distortion Giant arcs are the merging of
2 or 3 (or possibly more) multiple images
Giant arc in Cl2244-04, z2.24, Septuple image
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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.
Critical Line
Lensed pair in AC114, z1.86
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How to identify multiple images ?
RK Color image
Extreme similar colors
Example of a triple ERO system at z1.6 (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.
Abell 68 ERO triple image at z1.6
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How to identify multiple images ?
Color and Morphology Lens model can help for
the identification when different solution are
possible
Quintuple arc (z1.67) in Cl00241654 (z0.39)
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Strong Galaxy-Galaxy Lensing in Cluster

• Cluster Galaxies are breaking arcs into
  smaller ones, adding new images of the lensed
  galaxy.

Abell 2218, arc at z0.702, with 8
images identified (the arc is the merging of 2
images)
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Strong Lensing modeling strategy

• Cluster 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
Kneib et al 1996

• large scale cluster componentgalaxy halo
  components (starsDM)
• need to scale the galaxy halo components for
  example for a PIEMD mass distribution
• Hence

Constant M/L
FP scaling
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Maximum Likelihood expressions

• Likelihood 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 Hubble (color) images
Abell 2218 at z0.175
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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 lenses

• Single multiple image system degeneracy between
  the mass and the lens efficiency E

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Cosmography with clusters lenses

• TWO 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 lenses

• THREE 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 Prospects
Soucail, Kneib, Golse, 2004

• 4 multiple image systems at z0.7, 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!

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Critical requirements for cosmography with
Cluster Lenses

• Many multiple images with Spectroscopic redshift
  (gtinterest of IFS)
• Images with different redshifts
• Examples A2218 (z0.18) 10 systems, 5 with z,
  A1689 (z0.18) 30 systems, a few with z, A370
  (z0.37) 5 systems, 2 with z
• New Cl0152-05 (z0.83) 8 systems, 1 with z

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A potentially interesting new cluster
Cl0152-05 (z0.83) 8 multiple images
identified Only one with spectroscopic redshift
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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)

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END