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3D Cosmic Shear and darkCAM

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

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3D Cosmic Shear and darkCAM

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  1. 3D Cosmic Shear and darkCAM Alan Heavens Institute for Astronomy University of Edinburgh UK EDEN in Paris Dec 9 2005

  2. OUTLINE OF TALK: What effects of DE does lensing probe? Why 3D lensing? The darkCAM project

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

  4. 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

  5. Gravitational Lensing • Coherent distortion of background images • Shear, Magnification, Amplification θ β γ2 Van Waerbeke & Mellier 2004 γ1 Complex shear  =1 + i 2 e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966

  6. 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 Kamionkowski et al 1997 Kaiser 1998 Hu & Tegmark 1999 van Waerbeke et al 1999 (Flat Universe)

  7. g = g1 + ig2 Estimating shear • Ellipticity of galaxy e = e(intrinsic) + 2g • Estimate SHEARg by averaging over many galaxies Can also use MAGNIFICATION or AMPLIFICATION • Cosmic shear: ~1% distortions

  8. 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

  9. 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 lensinge = eI +   ee* = eIeI* + * + eI*

  10. eIeI*:Theory: Tidal torques Brown et al 2000 Heymans et al 2003 Heavens, Refregier & Heymans 2000, Croft & Metzler 2000, Crittenden et al 2001 etc 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

  11. 3D Lensing Heavens 2003 Why project at all? With distance information, we have a 3D SHEAR FIELD, sampled at various points. + z

  12. Tomography Hu 1999 Improves parameter estimation

  13. Real 1 imaginaryi2 Full 3D cosmic shear =1+i2 Hu • Shear is a spin-weight 2 field • Spin weight is s if under rotation of coordinate axes byψ, object changes from A to Aexp(isψ) • Lensing potential is a scalar spin-weight 0 field • Edthð raises spin-weight by 1 • cf CMB polarisation, but in 3D Castro, Heavens, Kitching Phys Rev D 2005

  14. Spectral analysis • In general, a spin-2 field can be written as =½ðð (E+i B) • B should be zero; =E. Very useful check on systematics • Natural expansion of (r): jl(kr) Ylm(θ, φ) •  Expand  in spin-weight 2 spherical harmonics 2Ylm(θ, φ) and spherical Bessel functions

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

  16. 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

  17. A901a A901b A902 3D Reconstruction Taylor 2001; Keaton, Hu • Potential Field: • Galaxy density: Taylor et al, 2004

  18. 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

  19. darkCAM on VISTA VISTA (Visible & Infrared Survey Telescope for Astronomy) 4 metre mirror

  20. 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)

  21. 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

  22. VISTA site • NTT Peak, near VLTs at Paranal • ~0.66” at 500nm

  23. 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.

  24. 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 0.11 error on wa w(a) =w0+(1-a)wa

  25. Observer Galaxy cluster/lens z1 zL z2 A Geometric Dark Energy Test r(z) only g1 g2 • 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)

  26. Prospects for darkCAM • Geometric test: • 3% on w0

  27. 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 • 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 • 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

  28. darkCAM 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

  29. Photo-z errors from COMBO-17 Wolf et al 2004

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

  31. 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

  32. 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

  33. 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 usefulfor the POWER SPECTRUM S/N for estimating power spectrum For Dark Energy properties there is much more from 3D Heavens 2003

  34. COMBO-17 field and team Christian Wolf, Klaus Meisenheimer, Andrea Borch, Simon Dye, Martina Kleinheinrich, Zoltan Kovacs, Lutz Wisotski and others 0.5 degree

  35. A901a A901b A902 Supercluster Abell 901/2 in COMBO-17 Survey • z=0.16 • R=24.5 • 17 bands • Δz<0.02 3Mpc/h (Gray et al., 2002)

  36. COMBO-17: Cosmology results (2D analysis) σ8 ( Ωm/0.27 )0.6 = 0.71 ± 0.11 Heymans, … AFH et al 2003 (Marginalised over h) • Free of intrinsic alignment systematic effect (~0.03)

  37. 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

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

  39. Dark Energy from Baryon Wiggles with darkCAM • Measure w from angular diameter of baryon wiggles with z.

  40. 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

  41. Lessons from the CMB • Physics is simple • Unaffected (mostly) by complicated astrophysics • Careful survey design Cosmic Shear surveys offer same possibilities

  42. 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

  43. 3D Lensing Theory: (Castro, Heavens & Kitching Phys Rev D 2005) Lensing Potential

  44. Real Imaginary Useful check on systematics

  45. Recent results: CFHTLS 22 sq deg; median z=0.8 Hoekstra et al 2005; see also Sembolini et al 2005

  46. 2-D Cosmic Shear Correlations van Waerbeke et al, 2005: Results from theVIRMOS-Descart Survey 2x10-4 10-4 0 0.6Mpc/h 6Mpc/h 30Mpc/h Shear correlations Signal Noise+systematics xE,B(q)

  47. Effects of lensing • Expansion + shear

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