VIEWS: 12 PAGES: 56 POSTED ON: 9/6/2011 Public Domain
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 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 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 γ2 Van Waerbeke & Mellier 2004 γ1 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 1999 Estimating shear Ellipticity of galaxy e = e(intrinsic) + 2 g Estimate SHEAR g by averaging over many galaxies g= g1 + ig2 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 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* + * + eI* Intrinsic alignments ee* = * + eIeI* + eI* 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 2000 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. +z Tomography Hu 1999 Improves parameter estimation Full 3D cosmic shear g=g1+ig2 Real g1 imaginaryig2 1 g (r) = ( x - i y )( x - i y ) (r) 2 1 Hu g (r ) = ðð (r ) 2 • 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 systematics Natural expansion of (r): jl(kr) Ylm(θ, φ) Expand g in spin-weight 2 spherical harmonics 2Ylm(θ, φ) and spherical Bessel functions Relationship to dark matter field: Small-angle surveys (Heavens & Kitching 2006 in prep) Distance to galaxy Weight Transform of the Integral nature of Include photo- Transform of shear field lensing z errors density field (nonlinear) 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 Taylor Potential Field: A901a A901b 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 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) PLANCK darkCAM Both 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 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 darkCAM (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 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 2D3D: improvement on error Fisher matrix analysis – P(k) Fractional Error improves error on from 1.4% to amplitude of 0.9% power spectrum Maximum l analysed For the matter power spectrum there is not much to be gained by going to 3D 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 Survey • z=0.16 • R=24.5 •17 bands A901a • Δz<0.02 A901b 3Mpc/h A902 (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 2003 (Marginalised • 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 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=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 astrophysics 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 Heavens 1997 1 -1 C -1 C -1 T T Fa = Trace C C +C + 2 a a 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 Signal correlations 2x10-4 Noise+systematics xE,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 2 2 ds 2 = 1 + 2 c 2 dt 2 - R 2 (t )1 - 2 dl 2 c c