3D%20Cosmic%20Shear%20and%20darkCAM

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3D Cosmic Shear and darkCAM

• Alan Heavens
• Institute for Astronomy
• University of Edinburgh UK
• EDEN in Paris Dec 9 2005

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OUTLINE OF TALK
What effects of DE does lensing probe? Why 3D
lensing? The darkCAM project
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Effects of w

• Distance-redshift relations
• r(z)
• Angular diameter distance DA
• Luminosity Distance DL
• Growth rate of perturbations g(z)

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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
  promising
• Probing both allows lifting of degeneracy between
  dark energy and modified gravity laws

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Gravitational Lensing

• Coherent distortion of background images
• Shear, Magnification, Amplification

?
ß
?2
Van Waerbeke Mellier 2004
?1
Complex shear ? ?1 i ?2
e.g. Gunn 1967 (Feynman 1964) Kristian Sachs
1966
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Shear, Dark Matter and cosmology

• Lensing potential f

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 Kamionkowski et al 1997 Kaiser 1998
Hu Tegmark 1999 van
Waerbeke et al 1999
(Flat Universe)
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Estimating shear

• Ellipticity of galaxy e e(intrinsic) 2
  g
• Estimate SHEAR g by averaging over many galaxies

Can also use MAGNIFICATION or AMPLIFICATION

• Cosmic shear 1 distortions

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2D weak lensing

• E.g. Shear-shear correlations on the sky
• Relate to nonlinear matter power spectrum
• 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 spectrum
Peacock, Dodds 96 Smith et al 2003
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Systematics physical

• Intrinsic alignments

• Lensing signal coherent distortion of
  background images
• Lensing analysis usually assumes orientations of
  source galaxies are uncorrelated
• Intrinsic correlations destroy this

Weak lensing e eI ? ? ?ee? ?eIeI? ????
??eI?
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Intrinsic alignments
?ee? ???? ?eIeI? ?eI??
Downweight/discard pairs with similar photometric
redshifts (Heymans Heavens 2002 King
Schneider 2002a,b) REMOVES EFFECT COMPLETELY
?eI?? ? Hirata Seljak 2004 Mandelbaum et al
2005 King 2005 B-modes template fitting
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3D Lensing
Heavens 2003
Why project at all? With distance information,
we have a 3D SHEAR FIELD, sampled at various
points.
z
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Tomography
Hu 1999
Improves parameter estimation
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Full 3D cosmic shear
??1i?2
Hu

• Shear is a spin-weight 2 field
• Spin weight is s if under rotation of coordinate
  axes by ?, object changes from A to Aexp(is?)
• 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
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Spectral analysis

• In general, a spin-2 field can be written as
• ?½ðð (?Ei ?B)
• ?B should be zero ??E. Very useful check on
  systematics
• Natural expansion of ?(r)
• jl(kr) Ylm(?, f)
• ? Expand ? in spin-weight 2 spherical harmonics
  2Ylm(?, f) and spherical Bessel functions

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Relationship to dark matter field
Small-angle surveys (Heavens Kitching 2006 in
prep)
Distance to galaxy
Weight
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3D lensing COMBO-17 survey

• WFI on ESO 2.2m
• 12 medium and 5 broad bands
• Very good image quality

Median z 0.6 4 x 0.25 square degree
Wolf, Meisenheimer et al
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3D Reconstruction
Taylor 2001 Keaton, Hu

• Potential Field
• Galaxy density

Taylor et al, 2004
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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
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darkCAM on VISTA
VISTA (Visible Infrared Survey Telescope for
Astronomy) 4 metre mirror
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darkCAM Camera

• 50 2k by 4k red-optimised CCDs
• 2 square degrees
• 0.23 pixels
• ADC
• Filters in gVrIz (no U)
• 15m
• Proposal to PPARC/ESO for 2009 start
• UK/French/German/Swiss collaboration (50 PPARC)

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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
• Designed for weak lensing
• Needs are demanding factor 10 more accurate
  than now

Ellipticity of PSF in 0.7 seeing
Angle from zenith/degrees
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VISTA site

• NTT Peak, near VLTs at Paranal
• 0.66 at 500nm

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Proposed darkCAM survey

• 10000 square degrees with ltzgt0.7
• Or 5000 square degrees with ltzgt0.8
• 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, 5s, 80 of flux within 1.6 aperture)
g25.9 r25.3 I24.7 z23.8.
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Expected errors from darkCAM survey 3D shear
transform (DA and g)
PLANCK darkCAM Both
With flat Planck prior 3 error on w0 1.5 on
w at z0.4 0.11 error on wa
w(a) w0(1-a)wa
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A Geometric Dark Energy Test r(z) only
g1 g2

• Depends only on global geometry of Universe OV,
  Om and w.
• Independent of structure.
• Apply to large signal from galaxy clusters.
• (Jain Taylor, 2003, Phys Rev Lett, 91,1302)

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Prospects for darkCAM

• Geometric test
• 3 on w0

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Wider Scientific goals of darkCAM
With a 10,000 sq deg, ltzgt0.7 survey can also
do. 1,000 square degrees with 9-band (IR)
photometry

• Weak strong lensing
• The Local Group
• Brown Dwarf detection
• White Dwarf detection
• Outer Solar System
• Near Earth Objects
• Studies of radio AGN
• Space sub-millimetre sources
• High-Redshift clusters
• Complement to Ha surveys
• Galaxy-galaxy lensing
• LISA complement
• DUNE complement

• Baryon wiggles
• SZ cluster studies
• Galaxy photometric redshift survey
• Galaxy evolution
• Galaxy clustering evolution
• Low-surface brightness galaxies
• Micro-Jansky radio sources
• Redshifts for X-ray clusters
• Sub-millimetre sources
• Star formation studies
• High-redshift quasar detection
• High-redshift quasar evolution
• Local galaxy studies
• QSO monitoring

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Conclusions

• UK/ESO currently have no astronomy projects
  focussing on accurate dark energy properties
• Lensing in 3D is very powerful accuracies of 2
  on w potentially possible
• Physical systematics can be controlled
  (intrinsic-lensing?)
• 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

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Photo-z errors from COMBO-17
Wolf et al 2004
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Galaxy Formation Environment
Photo-z select cluster galaxies SEDs Red
quiescent Blue star
forming
Gray et al 2004
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2D?3D improvement on error Fisher matrix
analysis P(k)
Error improves from 1.4 to 0.9
Fractional error on amplitude of power spectrum
Maximum l analysed
For the matter power spectrum there is not much
to be gained by going to 3D
Heavens 2003
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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

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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 few radial modes which are
useful for the POWER SPECTRUM
S/N for estimating power spectrum
For Dark Energy properties there is much more
from 3D
Heavens 2003
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COMBO-17 field and team
Christian Wolf, Klaus Meisenheimer, Andrea Borch,
Simon Dye, Martina Kleinheinrich, Zoltan Kovacs,
Lutz Wisotski and others
0.5 degree
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Supercluster Abell 901/2 in COMBO-17 Survey

• z0.16
• R24.5
• 17 bands
• ?zlt0.02

3Mpc/h
(Gray et al., 2002)
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COMBO-17 Cosmology results (2D analysis)
s 8 ( O m/0.27 )0.6 0.71 0.11
Heymans, AFH et al 2003
(Marginalised over h)

• Free of intrinsic alignment systematic effect
  (0.03)

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E and B modes
Lensing essentially produces only E modes
Refregier Jain Seljak
B modes from galaxy clustering, 2nd-order effects
(both small), imperfect PSF modelling, optics
systematics, intrinsic alignments of galaxies
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COMBO 17 preliminary 3D results

• First 3D shear power spectrum analysis
• Restricted mode set (at present)

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Dark Energy from Baryon Wiggles with darkCAM

• Measure w from angular diameter of baryon wiggles
  with z.

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Cosmology after WMAP

• Dark Matter/Dark Energy
• Is the DE a Cosmological Constant, or something
  else?
• Equation of state Pw?c2 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

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Lessons from the CMB

• Physics is simple
• Unaffected (mostly) by complicated astrophysics
• Careful survey design

Cosmic Shear surveys offer same possibilities
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Is the experiment worth it? Fisher Matrix
See Tegmark, Taylor and Heavens 1997
Fisher matrix gives best error you can
expect Error on parameter ??
- Analyse experimental design
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3D Lensing Theory (Castro, Heavens Kitching
Phys Rev D 2005)
Lensing Potential
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Real Imaginary
Useful check on systematics
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Recent results CFHTLS
22 sq deg median z0.8
Hoekstra et al 2005 see also Sembolini et al 2005
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2-D Cosmic Shear Correlations
van Waerbeke et al, 2005 Results from the
VIRMOS-Descart Survey
2x10-4 10-4 0
0.6Mpc/h
6Mpc/h 30Mpc/h
Shear correlations
Signal
Noisesystematics
xE,B(q)
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Effects of lensing

• Expansion shear

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Summary of spherical shear power spectrum
advantages
Expand lensing potential in spherical harmonics
and spherical Bessel functions
Spherical version of 3D Fourier Transform.
WHY? 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)
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WMAP2dFGRS results
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Major questions

• What is the Dark Matter?
• What is the Dark Energy/??

Scalar field? Quintessence
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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 controlled

• Weak lensing physics is even simpler
• Observables are predictable robustly ab initio
• Observables sensitive to equation of state of
  Dark Energy (with 3D analysis)
• Systematics controllable

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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 samples
• 3D weak lensing physics well understood needs
  very good control of optical quality

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Lensing physics