Probing the Dark Universe with Weak Gravitational Lensing
Probing the Dark Universe with Weak Gravitational Lensing Andy Taylor Institute for Astronomy, School of Physics, University of Edinburgh, Royal Observatory, Edinburgh, U. K. With David Bacon, Meghan Grey, Michael Brown, Tom Kitching, Chris Wolf, Klaus Meisenheimer, Bhuvnesh Jain 6/8/2021 IDM 2004, September, Edinburgh 1
The “Standard Model” of Cosmology • WMAP, SNIa, 2 d. FGRS, Sloan Digital Sky Survey: – – 70% Dark Energy 25% Dark Matter 5% Baryonic Matter Spatially flat • Four outstanding problems: – – Dark Matter Dark Energy Inflation Galaxy formation 6/8/2021 (VIRGO Consortium) 2 IDM 2004, September, Edinburgh
Gravitational Lensing • Hubble Space Telescope deep field of a galaxy cluster – the large gravitational lens, Abell 2218. 6/8/2021 IDM 2004, September, Edinburgh 3
Gravitational Lensing • A simple scattering experiment: Observer 6/8/2021 Galaxy cluster/lens IDM 2004, September, Edinburgh Background source 4
Gravitational Lens Distortions • Galaxy ellipticity, e: • Lensing effect: Shear matrix e’ = e + 2 g • On average <e> = 0. • So <e’ >=2 g. • Shear matrix: 6/8/2021 g = g 1 IDM 2004, September, Edinburgh + g 2 5
Weak Lensing • An observable is the shear (2 -d tidal) matrix: (Take derivatives on sky. ) • The 2 -d lensing scalar potential, f, is projected Newtonian potential, F: 6/8/2021 IDM 2004, September, Edinburgh a 6
Mapping the Dark Matter • From shear to projected density (Kaiser & Squires, 1993): Surface potential Surface density 6/8/2021 = S/Sc IDM 2004, September, Edinburgh (Courtesy A. Refregier)7
Supercluster Abell 901/2 in COMBO-17 Survey • z=0. 16 • R=24. 5 A 901 a A 901 b 1/2 deg 3 Mpc/h A 902 6/8/2021 IDM 2004, & September, Edinburgh 8 (Gray Taylor, et al. , 2002, Ap. J, 568, 141)
Mass and light in Supercluster A 901/2 Dark Matter contours, k. Elliptical galaxy light shading. 6/8/2021 Error: Dk=0. 02 (1 -contour) IDM 2004, & September, Edinburgh 9 (Gray Taylor, et al. , 2002, Ap. J, 568, 141)
Mapping the Dark Matter in 3 -D • The lens potential, f, is a radial integral over the 3 -D Newtonian potential, F: Observer 6/8/2021 Galaxy clusters/lenses IDM 2004, September, Edinburgh Background source 10
Mapping the Dark Matter in 3 -D • With source distances this can be exactly solved to recover the 3 -D Newtonian potential: (Taylor 2001) Observer 6/8/2021 Galaxy clusters/lenses IDM 2004, September, Edinburgh Background source 11
Is 3 -D dark matter mapping practical? • Shot-noise for 3 -D dark matter potential map: (Bacon & Taylor MN 2003; Taylor, et al MN 2004) • So Wiener filter in redshift: (Bacon & Taylor, 2003; Hu & Keeton, 2002) • Can now resolve clusters. • 3 -D lensing quality data already exists. . . COMB 0 -17 has 176/8/2021 band photometric. IDM 2004, redshifts Dz=0. 01. September, with Edinburgh 12
The 3 -D dark matter potential field • Potential Field: z 1. 0 A 901 a CB 1 A 901 b • Galaxy density: (2 -s threshold) 0. 6 0. 4 A 901 a Y A 902 6/8/2021 0. 8 X IDM 2004, September, Edinburgh A 902 13 Taylor, et al, 2004 MN, in press
The 3 -D dark matter potential and galaxy number density fields • Potential Field: • Galaxy number density: 6/8/2021 IDM 2004, September, Edinburgh 14 Taylor, et al, 2004 MN, in press
A 901/2 + CB 1 Cluster parameters Cluster Redshift A 901 a A 901 b A 902 CB 1 0. 16 0. 48 M (<0. 5 Mpc) (1013 Msun) 10. 8+-2 8. 4+-2 5. 1+-3 12. 0+-6 L(<0. 5 Mpc) M/L (1011 Lsun) (Msun/Lsun) 24. 7 43. 7 13. 6 62. 2 19. 5 26. 2 13. 0 92. 3 • Estimate projection-free masses of all objects. • Erratic mass-to-light ratio – non-equilibrium system. • Modelling with analytic and numerical methods. 6/8/2021 (Taylor, et al, 2004 MN, in press) IDM 2004, September, Edinburgh 15
Cosmic Shear • Lensing by the large-scale dark matter distribution. • First detected by 4 groups in 2000. 6/8/2021 IDM 2004, September, Edinburgh 16
Four random fields in COMBO-17 survey 2 -D Dark Matter Maps: Chandra Deep Field South Galactic Pole S 11 FDF • Area = 1 sq deg. • Depth: z = 0. 8. • Scale: 10 Mpc/h. 6/8/2021 IDM 2004, September, Edinburgh 17
Cosmic Shear Power Spectrum • Maximum Likelihood Analysis of Cosmic Shear. Measured over 4 random COMBO-17 fields. zm = 0. 85+/-0. 05 from photometric redshifts Shear Amplitude 50 R(Mpc/h) 5 0. 5 (signal) (noise) Standard LCDM model Multipoles 6/8/2021 IDM 2004, September, Edinburgh Brown, Taylor, et al, 2003, MNRAS, 341, 100 18
Results from Cosmic Shear • Combine with 2 d. F Galaxy Redshift Survey & pre-WMAP CMB 2 d. F s 8(Wm/0. 3)0. 49=0. 71+/-0. 09 Percival et al (2002)Lewis & Bridle (2002) s 8 = 0. 73+/-0. 05 WMAP GL Wm = 0. 27+/-0. 02 (h=0. 72, t=0. 1) Wm 6/8/2021 IDM 2004, September, Edinburgh Brown, Taylor, et al, 2003, MNRAS, 341, 100 19
3 -D Cosmic Shear • Shear probes the density field at different redshifts: Cosmology Shear-shear cross-power Observer Redshift 6/8/2021 IDM 2004, September, Edinburgh 20
The Growth of Dark Matter Clustering • Evolution of the matter power spectrum: 1 -sigma Pm(k, z) c 2 -fit to data. 2 -sigma First detection of evolution of Dark matter clustering. A fundamental prediction of Cosmology. 6/8/2021 LCDM Redshift IDM 2004, September, Edinburgh 21 (Bacon & Taylor, et al 2004, MN)
Geometric test of Dark Energy (Bhuvnesh Jain & AT, 2003, Phys Rev Lett, 91, 1302) n Depends only on WV, w = p/r (and Wm+WK). Observer 6/8/2021 Galaxy cluster/lens z. L IDM 2004, September, Edinburgh z 1 z 2 22
Geometric test of Dark Energy n Estimate parameters by minimising c 2 -fit over all source configurations. Observer 6/8/2021 Galaxy cluster/lens z. L IDM 2004, September, Edinburgh z 1 z 2 23
Geometric test of Dark Energy (with Tom Kitching and David Bacon) • • • Geometric test applied to A 901/2 clusters. Dw~0. 8 from 3 clusters. Uncertainty scales as: w A 901/2 WMAP WV • ~1% for dark. CAM on VISTA. 6/8/2021 IDM 2004, September, Edinburgh 24
Measuring the evolution of Dark Energy • Measure Wv and w(a)=w 0+wa(1 -a). • Estimate error for SNAP (zm=1. 5). • 10% of sky: Dw=~1%, Dwa=~10% wa=0 w 0 6/8/2021 wa WV IDM 2004, September, Edinburgh w 0 25 Jain & Taylor, Phys. Rev. Lett, 2003
dark. CAM on VISTA • Comparison of lensing telescopes grasp (area x fov) and timescales: VISTA (Visible & Infrared Survey Telescope for Astronomy) dark. CAM 6/8/2021 • Proposal to PPARC to start in 2009. (PI: Taylor) w to ~1% accuracy. IDM 2004, • September, Edinburgh 26 • 3 -D dark matter map of sky.
Summary • With 3 -D lensing (shear + redshifts) we can now measure the 3 -D Dark Matter distribution. • Detect the growth of Dark Matter clustering. • And measure the equation of state of dark energy. • Can measure dark energy properties in near future with dark. CAM on VISTA. 6/8/2021 IDM 2004, September, Edinburgh 27
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