3D weak lensing

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					3D Cosmic Shear and

          Alan Heavens
         Institute for Astronomy
         University of Edinburgh
        EDEN in Paris Dec 9 2005
OUTLINE OF TALK:   What effects of DE does lensing probe?
                   Why 3D lensing?
                   The darkCAM project
                Effects of w
 Distance-redshift relations
   r(z)
   Angular diameter distance DA
   Luminosity Distance DL
 Growth rate of perturbations g(z)
             Detection of w(z)
 Various methods
     3D weak lensing (DA, and g)
     Baryon wiggles (DA)
     Supernova Hubble diagram (DL)
     Cluster abundance vs z (g)
 Independent, but 3D weak lensing is the most
 Probing both allows lifting of degeneracy
  between dark energy and modified gravity laws
            Gravitational Lensing
 Coherent distortion of
  background images
 Shear, Magnification,
                                        Van Waerbeke &
                                        Mellier 2004


e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966     Complex shear  =1 + i
  Shear, Dark Matter and cosmology
  Lensing potential φ                                Statistics of distortions:
                                                      Miralda-Escudé 1991 Blandford
                                                      et al 1991 Babul & Lee 1991
                                                      Kaiser 1992

Lensing potential related to peculiar gravitational
potential by                                          Tool for cosmology: Bernardeau
                                                      et al 1997 Jain & Seljak 1997
(Flat                                                 Kamionkowski et al 1997 Kaiser
                                                      1998            Hu & Tegmark
Universe)                                             1999 van Waerbeke et al
                   Estimating shear
 Ellipticity of galaxy
  e = e(intrinsic) + 2 g
 Estimate SHEAR g by
  averaging over many

     g=       g1       +    ig2

 • Cosmic shear: ~1% distortions
                   2D weak lensing
 E.g. Shear-shear correlations on the sky
 Relate to nonlinear matter power
 Need to know redshift distribution of
  sources – via photo-zs

                                           Simulated: Jain et al 2000

   Number density of
   sources (photo-zs)
                            3D nonlinear
                            matter power
                                             Peacock, Dodds 96;
                                             Smith et al 2003
             Systematics: physical
                            Intrinsic alignments
• Lensing signal:
coherent distortion of
background images
• Lensing analysis
usually assumes
orientations of source
galaxies are
uncorrelated                 Weak lensing e = eI + 
• Intrinsic correlations
destroy this
                              ee* = eIeI* + * +
               Intrinsic alignments
             ee* = * + eIeI* +
   eIeI*: Theory: Tidal torques

                                             Downweight/discard pairs
                                             with similar photometric
                                             redshifts (Heymans & Heavens
                                             2002; King & Schneider 2002a,b)
Heavens, Refregier & Heymans 2000, Croft &   REMOVES EFFECT
Metzler 2000, Crittenden et al 2001 etc      ~COMPLETELY

                Brown et al
                                                  eI* ? Hirata &
                                                  Seljak 2004; Mandelbaum
                    Heymans                       et al 2005 King 2005
                    et al 2003
                                                  B-modes; template fitting
            3D Lensing
                                Heavens 2003

Why project at all?

With distance information, we
have a 3D SHEAR FIELD,
sampled at various points.


                                Hu 1999

Improves parameter estimation
          Full 3D cosmic shear
                                    Real g1 imaginaryig2

                                     g (r) = ( x - i y )( x - i y ) (r)
Hu                                  g (r ) = ðð (r )
• Shear is a spin-weight 2 field
• Spin weight is s if under rotation of coordinate axes by ψ, object
changes from A to Aexp(isψ)
• Lensing potential  is a scalar spin-weight 0 field
• Edth ð raises spin-weight by 1
• cf CMB polarisation, but in 3D          Castro, Heavens, Kitching Phys Rev D 2005
            Spectral analysis
 In general, a spin-2 field can be written as
                  g=½ðð (E+i B)
 B should be zero; =E. Very useful check on

 Natural expansion of (r):
            jl(kr) Ylm(θ, φ)
  Expand g in spin-weight 2 spherical
  harmonics 2Ylm(θ, φ) and spherical Bessel
    Relationship to dark matter field:
     Small-angle surveys (Heavens & Kitching 2006 in prep)

                                                      Distance to galaxy


Transform of the
                    Integral nature of    Include photo-     Transform of
shear field
                    lensing               z errors           density field
3D lensing: COMBO-17 survey
 WFI on ESO 2.2m
 12 medium and 5 broad bands
 Very good image quality

     z                                   Median z ~ 0.6; 4 x
         = 0.015
    1+ z                                  0.25 square degree
                   Wolf, Meisenheimer et al
                  3D Reconstruction 2001; Keaton, Hu

 Potential


 Galaxy
    Taylor et al, 2004
First 3D power spectrum analysis:
  Dark Energy from COMBO-17

                    • Conditional error only
                    • w = -1.0 ± 0.6
                    • From 0.5 square
                    degrees only
                    • Completely preliminary

                        Kitching & Heavens in prep
           darkCAM on VISTA

(Visible & Infrared Survey
Telescope for Astronomy)
      4 metre mirror
           darkCAM Camera
 50 2k by 4k red-optimised CCDs
 2 square degrees
 0.23” pixels
 Filters in g’Vr’I’z’ (no U)
 €15m
 Proposal to PPARC/ESO for 2009
 UK/French/German/Swiss
  collaboration (50% PPARC)
                 VISTA telescope
 Designed to take an IR and a
    visible camera
   f/1 primary
   Continuous focus monitoring
   Active control
   0-2% PSF distortions over focal
    plane, all positions            Ellipticity
   Designed for weak lensing       of PSF
                                    in 0.7”
   Needs are demanding: ~factor seeing
    10 more accurate than now

                                                  Angle from zenith/degrees
               VISTA site
 NTT Peak, near
  VLTs at Paranal
 ~0.66” at 500nm
     Proposed darkCAM survey
 10000 square degrees with <z>=0.7
 Or 5000 square degrees with <z>=0.8
 1000 square degrees may have 9-band photometry, with
  IR as well (not assumed)
 Data processing via VISTA pipeline at CASU, archiving
  at WFAU

   Limiting AB magnitudes (15 min
   exposures, 0.7” seeing, 5σ, 80% of
   flux within 1.6” aperture):
   g’=25.9 r’=25.3
   I’=24.7 z’=23.8.
Expected errors from darkCAM survey:
   3D shear transform (DA and g)


   With flat Planck prior:
   3% error on w0
   1.5% on w at z~0.4
                             w(a) =w0+(1-a)wa
   0.11 error on wa
           A Geometric Dark Energy Test
                     r(z) only
     The ratio of shears has a purely geometric dependence
                     g ( z1 , z L )       r ( z2 )[r ( z1 ) - r ( z L )]
    R(V , m , w) =                , R =
                     g ( z2 , z L )       r ( z1 )[r ( z2 ) - r ( z L )]
                                                                                  g1   g2

        Observer                    Galaxy cluster/lens
                                         zL                                  z1             z2

   Depends only on global geometry of Universe: ΩV, Ωm and w.
   Independent of structure.
   Apply to large signal from galaxy clusters.
                             (Jain & Taylor, 2003, Phys Rev Lett, 91,1302)
      Prospects for darkCAM
 Geometric test:
 3% on w0
 Wider Scientific goals of darkCAM
 With a 10,000 sq deg, <z>=0.7 survey can also do.
 1,000 square degrees with 9-band (+IR) photometry
 Baryon wiggles                      Weak & strong lensing
 SZ cluster studies                  The Local Group
 Galaxy photometric redshift survey  Brown Dwarf detection
 Galaxy evolution                    White Dwarf detection
 Galaxy clustering evolution         Outer Solar System
 Low-surface brightness galaxies     Near Earth Objects
 Micro-Jansky radio sources          Studies of radio AGN
 Redshifts for X-ray clusters        Space sub-millimetre sources
 Sub-millimetre sources              High-Redshift clusters
 Star formation studies              Complement to Ha surveys
 High-redshift quasar detection      Galaxy-galaxy lensing
 High-redshift quasar evolution      LISA complement
 Local galaxy studies                DUNE complement
 QSO monitoring
 UK/ESO currently have no astronomy
   projects focussing on accurate dark energy

 Lensing in 3D is very powerful: accuracies of
   ~2% on w potentially possible

 Physical systematics can be controlled          darkCAM

 Large-scale photometric redshift survey with
   extremely good image quality is needed

 darkCAM/VISTA is an extremely attractive
   option, custom designed for lensing

 Synergy with DUNE in longer term
Photo-z errors from COMBO-17

                  Wolf et al 2004
          Galaxy Formation & Environment
Photo-z: select cluster
SEDs:   Red – quiescent
        Blue – star forming

        Gray et al 2004
      2D3D: improvement on error
       Fisher matrix analysis – P(k)

Fractional                               Error improves
error on                                 from 1.4% to
amplitude of                             0.9%

               Maximum l analysed

  For the matter power spectrum there
  is not much to be gained by going to
                                                  Heavens 2003
     Signal-to-Noise eigenmodes

 3D analysis may be
    computational costly
    (comparable to CMB analysis)
   Some modes will be NOISY,
    some will be CORRELATED
   Can throw some data away,
    without losing much information
   How to do it in a sensible way…
   Instructive
       Karhünen-Loève analysis

     Form linear combinations of the shear expansion
     coefficients, which are UNCORRELATED, and
     ordered in USELESSNESS
                                                      See e.g. Tegmark, Taylor
                                                      and Heavens 1997

                                                     There are typically a
S/N for                                              few radial modes
estimating                                           which are useful for
power                                                the POWER
spectrum                                             SPECTRUM

    For Dark Energy properties there is much more from 3D
                                                              Heavens 2003
COMBO-17 field and team
                Christian Wolf, Klaus Meisenheimer,
                Andrea Borch, Simon Dye, Martina
                Kleinheinrich, Zoltan Kovacs, Lutz
                Wisotski and others

   0.5 degree
   Supercluster Abell 901/2 in COMBO-17

                                       • z=0.16
                                       • R=24.5
                                       •17 bands
                                       • Δz<0.02


              (Gray et al., 2002)
        COMBO-17: Cosmology results
              (2D analysis)

Heymans, … AFH et al             σ 8 ( Ω m/0.27 )0.6 = 0.71 ± 0.11
       • Free of intrinsic alignment systematic effect (~0.03)
                                                                 over h)
                    E and B modes

Lensing essentially produces     Refregier          Jain & Seljak

only E modes                   B modes from galaxy clustering, 2nd-
                               order effects (both small), imperfect
                               PSF modelling, optics systematics,
                               intrinsic alignments of galaxies
    COMBO 17 – preliminary 3D
 First 3D
  shear power
 Restricted
  mode set (at
      Dark Energy from Baryon Wiggles with
 Measure w from angular diameter of baryon wiggles
  with z.
                 after WMAP
 Dark Matter/Dark Energy
• Is the DE a Cosmological Constant, or something

• Equation of state: P=wρc2 w(z) ~ -1

• (How) does w evolve?

• CMB has limited sensitivity to w

• Weak Gravitational Lensing may be the best method
for constraining Dark Energy
       Lessons from the CMB
 Physics is simple
 Unaffected (mostly) by complicated
 Careful survey design

Cosmic Shear surveys offer same possibilities
Is the experiment worth it?
Fisher Matrix
                                           2 ln L       See
                                  Fa  -
                                          a         Tegmark,
                                                         Taylor and
                1       -1 C -1 C         
                                          -1   
                                                          T     
           Fa = Trace C       C      +C              +            
                2          a                  a     
                                             a                   

  Fisher matrix gives best error you can
  Error on parameter : a  (F -1 )aa

  - Analyse experimental design
3D Lensing
(Castro, Heavens
& Kitching Phys
Rev D 2005)

Lensing Potential
   Real    Imaginary

Useful check on
         Recent results: CFHTLS

             22 sq deg; median z=0.8

Hoekstra et al 2005; see also
Sembolini et al 2005
        2-D Cosmic Shear Correlations
van Waerbeke et al, 2005: Results from the VIRMOS-Descart Survey
                          0.6Mpc/h      6Mpc/h     30Mpc/h

   Shear                                         Signal
correlations   2x10-4

         xE,B()   10-4

          Effects of lensing
 Expansion + shear
    Summary of spherical shear
    power spectrum advantages
Expand lensing
potential in spherical
harmonics and spherical
Bessel functions
                          Spherical version of 3D Fourier Transform.
                          Lensing depends on r
                          Selection depends on sky position and r
                          Photo-z  radial error
                          Lensing – mass relation is relatively simple
                          Spectral: avoid highly nonlinear regime (high k)
WMAP+2dFGRS results
            Major questions
 What is the Dark Matter?
 What is the Dark Energy/Λ?

 G - g  = T
 G = T + g 
                               Scalar field? Quintessence:
         CMB and Cosmic Shear
 CMB has had phenomenal success
  because Physics of the CMB is well-
  understood and simple.
   CMB observables are sensitive to
    cosmological parameters
   Systematics (e.g. foregrounds) can be

 Weak   lensing physics is even simpler
    Observables are predictable robustly ab
    Observables sensitive to equation of state
   of Dark Energy (with 3D analysis)
    Systematics controllable
            Pros and cons
 Supernovae: standard candles?
 Clusters: physics far from understood
 Baryon wiggles: trust that wiggles in
  matter spectrum are reflected in galaxy
  power spectrum; need very large, deep
 3D weak lensing: physics well understood;
  needs very good control of optical quality
Lensing physics

             2                       2 
     ds 2 = 1 + 2 c 2 dt 2 - R 2 (t )1 - 2 dl 2
               c                        c 