Constraining Cosmography with Cluster Lenses Jean-Paul Kneib Laboratoire d’Astrophysique de Marseille

19 Sept. 2005JP KNEIB -- Dark Universe2 PLAN Quick introduction of cluster strong lensing How to find multiple images ? How do we constrain cosmology ? Future prospects

19 Sept. 2005JP KNEIB -- Dark Universe3 Historical Perspective 1986/1987: discovery of the giant luminous Arcs in Cl2244 and Abell : CFHT 1996: WFPC2

19 Sept. 2005JP KNEIB -- Dark Universe4 Lensing Theory The Context:

19 Sept. 2005JP KNEIB -- Dark Universe5 Cluster Lenses 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

19 Sept. 2005JP KNEIB -- Dark Universe6 Lensing Equations Notations: cosmology

19 Sept. 2005JP KNEIB -- Dark Universe7 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:

19 Sept. 2005JP KNEIB -- Dark Universe8 Lensing Equations Lens Mapping:  : lensing potential  Link with catastrophe theory  Purely geometrical: Achromatic effect Lens Efficiency

19 Sept. 2005JP KNEIB -- Dark Universe9 Redshift and Cosmology Lens Efficiency: For a fixed lens redshift, the lens efficiency increase with source redshift Weak cosmology dependence

19 Sept. 2005JP KNEIB -- Dark Universe10 Lensing Equations Lens Mapping distortion (first order): In polar coordinates:

19 Sept. 2005JP KNEIB -- Dark Universe11 Lensing Equations Amplification Matrix:  : convergence  : shear vector Reduced shear:

19 Sept. 2005JP KNEIB -- Dark Universe12 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)

19 Sept. 2005JP KNEIB -- Dark Universe13 Lensing Theory Multiple image configurations for a non- singular elliptical mass distribution Cusp arc Fold arcEinstein cross Radial arc Single imageSource

19 Sept. 2005JP KNEIB -- Dark Universe14 Strong Lensing Lensing equation can have multiple solution: Finding source is easy! Finding the images need solving a 2D equation (ray tracing)

19 Sept. 2005JP KNEIB -- Dark Universe15 Lens 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 !! [A1689 with ACS => deep JWST observations] 30 triples: 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)

19 Sept. 2005JP KNEIB -- Dark Universe16 How to identify multiple images ? Extreme distortion: Giant arcs are the merging of 2 or 3 (or possibly more) multiple images Giant arc in Cl , z=2.24, Septuple image

19 Sept. 2005JP KNEIB -- Dark Universe17 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

19 Sept. 2005JP KNEIB -- Dark Universe18 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

19 Sept. 2005JP KNEIB -- Dark Universe19 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) in Cl (z=0.39)

19 Sept. 2005JP KNEIB -- Dark Universe20 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 z=0.702, with 8 images identified (the arc is the merging of 2 images)

19 Sept. 2005JP KNEIB -- Dark Universe21 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)

19 Sept. 2005JP KNEIB -- Dark Universe22 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: Constant M/L FP scaling Kneib et al 1996

19 Sept. 2005JP KNEIB -- Dark Universe23 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 :

19 Sept. 2005JP KNEIB -- Dark Universe24 Best strong lensing data: Hubble (color) images Abell 2218 at z=0.175

19 Sept. 2005JP KNEIB -- Dark Universe25 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

19 Sept. 2005JP KNEIB -- Dark Universe26 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

19 Sept. 2005JP KNEIB -- Dark Universe27 Cosmography with clusters lenses Lensing efficiency: Lens equation:

19 Sept. 2005JP KNEIB -- Dark Universe28 Cosmography with clusters lenses Single multiple image system: degeneracy between the mass and the lens efficiency E:

19 Sept. 2005JP KNEIB -- Dark Universe29 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:

19 Sept. 2005JP KNEIB -- Dark Universe30 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

19 Sept. 2005JP KNEIB -- Dark Universe31 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)

19 Sept. 2005JP KNEIB -- Dark Universe32 Results from A2218 & 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

19 Sept. 2005JP KNEIB -- Dark Universe33 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: Cl (z=0.83): 8 systems, 1 with z

19 Sept. 2005JP KNEIB -- Dark Universe34 A potentially interesting new cluster Cl (z=0.83) 8 multiple images identified Only one with spectroscopic redshift

19 Sept. 2005JP KNEIB -- Dark Universe35 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)

19 Sept. 2005JP KNEIB -- Dark Universe36 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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