3D Cosmic Shear and darkCAM

Alan Heavens

Institute for Astronomy University of Edinburgh UK 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 D A Luminosity Distance D L Growth rate of perturbations g(z)

Detection of w(z)

 Various methods     3D weak lensing ( D A , and g ) Baryon wiggles ( D A ) Supernova Hubble diagram ( D L ) 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

Gravitational Lensing

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

θ β

γ 2 Van Waerbeke & Mellier 2004 γ 1 e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966 Complex shear   2 =  1 + i

Shear, Dark Matter and cosmology  Lensing potential φ Statistics of distortions: Miralda-Escud é 1991 Blandford et al 1991 Babul & Lee 1991 Kaiser 1992 Lensing potential related to peculiar gravitational potential by (Flat Universe) Tool for cosmology: Bernardeau et al 1997 Jain & Seljak 1997 Kamionkowski et al 1997 Kaiser 1998 Hu & Tegmark 1999 van Waerbeke et al 1999

Estimating shear

  Ellipticity of galaxy e = e(intrinsic) + 2 g Estimate SHEAR g by averaging over many galaxies g = g 1 + i g 2 Can also use MAGNIFICATION or AMPLIFICATION • Cosmic shear: ~1% distortions

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

Systematics: physical

• Lensing signal: coherent distortion of background images • Lensing analysis usually assumes orientations of source galaxies are uncorrelated • Intrinsic correlations destroy this  Intrinsic alignments Weak lensing e = e I +    ee*   e I *  =  e I e I *  +  *  +



Intrinsic alignments

 e I e I *  :  ee*  =  *   e I  *  +  e I e I *  + Theory: Tidal torques Heavens, Refregier & Heymans 2000, Croft & Metzler 2000, Crittenden et al 2001 etc Brown et al 2000 Downweight/discard pairs with similar photometric redshifts (Heymans & Heavens 2002; King & Schneider 2002a,b) REMOVES EFFECT ~COMPLETELY Heymans et al 2003  e I  *  ?

Hirata & Seljak 2004; Mandelbaum et al 2005 King 2005 B-modes; template fitting

3D Lensing

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

Heavens 2003 + z

Tomography

Hu 1999 Improves parameter estimation

Full 3D cosmic shear

g = g 1 +i g 2 Real g 1 imaginary i g 2 Hu g (

r

) = 1 2 ( 

x



i



y

)( 

x



i



y

)  (

r

) g (

r

) = 1 2 ðð  (

r

) • Shear is a spin-weight 2 field • Spin weight is s if under rotation of coordinate axes by changes from A to Aexp(i s ψ ) ψ, object • 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 = ½ ðð (  E +i  B )  B should be zero;  =  E . Very useful check on systematics   Natural expansion of  (

r

): 

l

j (kr) Y lm ( θ, φ) Expand harmonics 2 Y lm ( θ, φ) functions g in spin-weight 2 spherical and spherical Bessel

Relationship to dark matter field: Small-angle surveys (Heavens & Kitching 2006 in prep) Distance to galaxy Weight Transform of the shear field Integral nature of lensing Include photo-z errors Transform of density field (nonlinear)

3D lensing: COMBO-17 survey

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

z

1 +

z

= 0 .

015 Wolf, Meisenheimer et al Median z ~ 0.6; 4 x 0.25 square degree

 Potential Field: A901a A901b

3D Reconstruction

Taylor 2001; Keaton, Hu  A902 Galaxy density: 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

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 ADC Filters in g’Vr’I’z’ (no U) €15m Proposal to PPARC/ESO for 2009 start 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 Designed for weak lensing Needs are demanding: ~factor Ellipticity of PSF in 0.7” seeing 10 more accurate than now Angle from zenith/degrees

  NTT Peak, near VLTs at Paranal ~0.66” at 500nm

VISTA site

Proposed darkCAM survey

    10000 square degrees with =0.7

Or 5000 square degrees with =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 (D A and g)

PLANCK darkCAM Both

With flat Planck prior: 3% error on w 0 1.5% on w at z~0.4

0.11 error on w a w(a) =w 0 +(1-a)w a

A Geometric Dark Energy Test r(z) only The ratio of shears has a purely geometric dependence

R

( 

V

, 

m

,

w

) = g g (

z

1 , (

z

2 ,

z L

)

z L

) , R =

r

(

z

2 )[

r

(

z

1 ) 

r

(

z

1 )[

r

(

z

2 ) 

r

(

z L

)]

r

(

z L

)] g 1 g 2 Observer Galaxy cluster/lens z L z 1 z 2    Depends only on global geometry of Universe: Ω V , Ω m 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 w 0

Wider Scientific goals of

darkCAM

              With a 10,000 sq deg, =0.7 survey can also do.

1,000 square degrees with 9-band (+IR) photometry 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              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 H a surveys Galaxy-galaxy lensing LISA complement DUNE complement QSO monitoring

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 darkCAM

Photo-z errors from COMBO-17

Wolf et al 2004

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

2D  3D: improvement on error Fisher matrix analysis – P(k) 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 Error improves from 1.4% to 0.9% 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

Karh

ü

nen-Lo

è

ve analysis

Form linear combinations of the shear expansion coefficients, which are UNCORRELATED , and ordered in USELESSNESS See e.g. Tegmark, Taylor and Heavens 1997 S/N for estimating power spectrum There are typically a few radial modes which are useful for the POWER 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 Survey A901a A901b • z=0.16 • R=24.5

•17 bands • Δz<0.02

3Mpc/h A902 (Gray et al., 2002)

COMBO-17: Cosmology results (2D analysis) Heymans, … AFH et al 2003 σ 8 ( Ω m /0.27 ) 0.6

• Free of intrinsic alignment systematic effect (~0.03) = 0.71 ± 0.11

(Marginalised over h)

E and B modes

Lensing essentially produces only E modes Refregier Jain & Seljak B modes from galaxy clustering, 2 PSF modelling, optics systematics, intrinsic alignments of galaxies nd order effects (both small), imperfect

COMBO 17 – preliminary 3D results  First 3D shear power spectrum analysis  Restricted mode set (at present)

Dark Energy from Baryon Wiggles with

darkCAM

 Measure

w

from angular diameter of baryon wiggles with

z

.

Cosmology after WMAP Dark Matter/Dark Energy • Is the DE a Cosmological Constant, or something else?

• Equation of state: P= w ρc 2 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 astrophysics  Careful survey design Cosmic Shear surveys offer same possibilities

Is the experiment worth it? Fisher Matrix

F

a

F

a = 1 2

Trace

  

C

 1   

C

a

C

 1   

C

     2  a ln  

L

 +

C

 1     a See Tegmark, Taylor and Heavens 1997  

T

   +  

T

  a           Fisher matrix gives best error you can expect: Error on parameter   :  a  (

F

 1 ) aa - Analyse experimental design

3D Lensing Theory: (Castro, Heavens & Kitching Phys Rev D 2005) Lensing Potential

Real Imaginary Useful check on systematics

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 correlations 2x10 -4 Signal Noise+systematics x E,B () 10 -4 0

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.

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)

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 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

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

Lensing physics

ds

2 = 1 + 2 

c

2

c

2

dt

2 

R

2 (

t

 )  1  2 

c

2

dl

2