Transcript 3D weak lensing - University of Groningen

Dark Energy with 3D
Cosmic Shear
Alan Heavens
Institute for Astronomy
University of Edinburgh
UK
with Tom Kitching, Patricia Castro,
Andy Taylor, Catherine Heymans et al
Bernard Jones. Valencia
30/06/06
Outline
 Dark Energy, Dark Matter
 Weak lensing
 3D weak lensing Statistical and
systematics control
 First 3D results from COMBO-17
 Future
Bernard and lensing
Major questions
 What is the Dark Matter?
 What is the Dark Energy/Λ?
G  g  T
G  T  g
Scalar field? Quintessence:
Detection of w(z)
 Effects of w: distance-redshift relation r(z), and growth
rate g
 Various methods
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
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
Supernova Hubble diagram (DL)
Baryon wiggles (DA)
Cluster abundance vs z (g)
3D weak lensing (r(z), and g)
 Probing both r(z) and g may allow lifting of degeneracy
between dark energy and modified gravity law
 3D weak lensing: physics well understood; needs
excellent optical quality
Gravitational Lensing
 Coherent distortion of
background images
 Shear, Magnification,
Amplification
θ
β
Van Waerbeke
& Mellier 2004
2
1
e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966
Complex shear  =1 + i
Shear, Dark Matter and Cosmology
 Lensing potential φ
Lensing potential related to peculiar gravitational
potential by
(Flat
Universe)
Estimating shear
 Ellipticity of galaxy
e = e(intrinsic) + g
 Cosmic shear: ~1%
distortions
 Estimate g by
averaging over many
galaxies
2D weak lensing
 E.g. Shear-shear correlations on the sky
 Theoretically related to nonlinear matter
power spectrum
Number density of
sources (photo-zs)
Simulated: Jain et al 2000
3D nonlinear
matter power
spectrum
 Need to know redshift distribution of
sources – photo-zs
Peacock, Dodds 96;
Smith et al 2003
Recent results: CFHTLS
22 sq deg; median z=0.8
Hoekstra et al 2005; see also
Semboloni et al 2005
What are the fundamental
limitations?
 Intrinsic alignments ?
• Lensing signal:
coherent distortion of
background images
• Lensing analysis
assumes orientations of
source galaxies are
uncorrelated
• Intrinsic correlations
destroy this
Weak lensing e = eI + 
 ee* = eIe*I +
*
Intrinsic alignments

ee* = * + eIeI* +
2eI*
eIeI*: Theory: Tidal torques
Heavens, Refregier & Heymans 2000,
Croft & Metzler 2000, Crittenden et al
2001 etc
Observations (SuperCOSMOS) Brown
et al 2001
Downweight/discard
pairs with similar
photometric redshifts
(Heymans & Heavens 2002; King &
Schneider 2002a,b)
REMOVES EFFECT
~COMPLETELY
Efstathiou & Jones 1979
 1000 particle simulations
Shear-intrinsic alignments ‹eγ*›
 Tidal field contributes to weak shear (of background)
 Tidal field could also orient galaxies (locally)
(Hirata & Seljak
2004; Mandelbaum et al 2005, Trujillo et al 2006, Yang et al 2006)
SDSS: Mandelbaum et al 2005
Theory: Heymans, AFH et al 2006
Expect 5-10% contamination
Removing contamination
 Intrinsic-intrinsic removal is easy (with zs)
 Shear-intrinsic is harder. However:
 massive galaxies largely responsible
 If present, it gives a B-mode signature
 Redshift-dependence is as expected:
Contamination signal
proportional to
DL DLS/DS
Heymans, AFH et al 2006
Aid to removal
King 2005 - template fitting
3D Lensing
Why project at all?
With distance information, we have a 3D SHEAR
FIELD, sampled at various points.
+z
2½D lensing in slices
Dividing the source distribution
improves parameter estimation
Hu 1999
3D cosmic shear
g = g1+ig2
Real g1
imag ig2
1
2
g (r )  ( x  i y )(  x  i y ) (r )
1
g (r )  ðð (r )
2
• Shear is a spin-weight 2 field
• Spin weight is s: under rotation of
coordinate axes by ψ, A → Aexp(isψ)
• In general, a spin-weight 2 field can be
written as
g=½ðð (E+i B)
Castro, AFH, Kitching Phys Rev D 2005
Relationship to dark matter field:
Natural expansion of shear is spherical Bessel functions and spin-weight
2 spherical harmonics. For small-angle surveys (Heavens, Kitching &
Taylor astroph Monday)
Transform
of the
shear
field
g i (k ,  x ,  y ) 
2

g
g
(r , ) j (kr) X  exp(i. )
galaxiesg

g (k , )  H 02 m  dz dzp p( z p | z ) n( z ) j (kr)
0
r(z)

0
1 1 
dr'    (1  z ' )  dk' j (k ' r ' )  (k ' , ; t ' )
 r r' 
Integral nature
of lensing
z and r
Include
photo-z
errors
Transform of
density field
Combination with other experiments
 CMB: Planck
 BAO: WFMOS 2000 sq deg to z=1
 SNe: 2000 to z=1.5
Planck + 3D WL
Combining 3D lensing, CMB, BAO,
SNe
DARK ENERGY: Assume w(a)=w0+wa(1-a)
3.5% accuracy on w at z=0
~1% on w(z) at z~0.4
Geometric Dark Energy Test
T heratioof shears has a purely geometricdependence
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
Observer


Galaxy cluster/lens
zL
z1
g2
z2
Depends only on global geometry of Universe: ΩV, Ωm and w.
Independent of structure.
(Jain & Taylor, 2003, Taylor, Kitching, Bacon, AFH astroph last week)
Systematics
 Can marginalise over ‘nuisance’ parameters, such as a
bias in the photo-zs
 Quick check on such errors from expected shift of
maximum likelihood point:
F=Generalised
Fisher matrix
Kim et al 2004; Taylor et al 2006; Heavens et al
2006
 Shift in estimate of w ~ 1.2 x mean error in photo-zs
(Shear ratio is more affected: 9 x)
 3D shear power seems less sensitive to this error than
tomography (Huterer et al 2005, Ma et al 2005)
 May require fewer calibrating spectroscopic redshifts
Conclusions
 Dark Energy and Dark Matter are now
key scientific goals of cosmology
 Lensing in 3D is very powerful:
accuracies of ~1-3% on w potentially
possible
 Physical systematics can be controlled
 Large-scale photometric redshift survey
with extremely good image quality is
needed ~10000 sq deg, median z~0.7
 Space (imaging) + ground (photozs)