1. 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
11/15/2018
IDM2004, September, Edinburgh

2. The “Standard Model” of Cosmology
WMAP, SNIa, 2dFGRS, 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
Cosmic Web – bottom up scenario – clusters then filaments then walls (membranes).
Note that filaments not well traced by galaxies & too ephemeral to emit x-rays, so lensing only way to detect.
(VIRGO Consortium)
11/15/2018
IDM2004, September, Edinburgh

3. Gravitational Lensing
Hubble Space Telescope deep field of a galaxy cluster – the large gravitational lens, Abell 2218.
Cosmic Web – bottom up scenario – clusters then filaments then walls (membranes).
Note that filaments not well traced by galaxies & too ephemeral to emit x-rays, so lensing only way to detect.
11/15/2018
IDM2004, September, Edinburgh

4. Gravitational Lensing
A simple scattering experiment:
Observer
Galaxy cluster/lens
Background source
11/15/2018
IDM2004, September, Edinburgh

5. Gravitational Lens Distortions
Galaxy ellipticity, e:
Lensing effect:
e’ = e + 2 g
On average <e> = 0.
So <e’ >=2g.
Shear matrix:
Shear matrix
Shear matrix
Define kappa and gamma
Mass sheet degeneracy
g = g g2
11/15/2018
IDM2004, September, Edinburgh

6. IDM2004, September, Edinburgh
Weak Lensing
An observable is the shear (2-d tidal) matrix:
The 2-d lensing scalar potential, f, is a projected Newtonian potential, F:
(Take derivatives
on sky.)
11/15/2018
IDM2004, September, Edinburgh

7. Mapping the Dark Matter
From shear to projected density (Kaiser & Squires, 1993):
Surface potential
Surface density
= S/Sc
(Courtesy A. Refregier)
11/15/2018
IDM2004, September, Edinburgh

8. Supercluster Abell 901/2 in COMBO-17 Survey
z=0.16
R=24.5
A901a
A901b
A902
1/2 deg
3Mpc/h
(Gray & Taylor, et al., 2002, ApJ, 568,141)
11/15/2018
IDM2004, September, Edinburgh

9. Mass and light in Supercluster A901/2
Dark Matter contours, k.
Elliptical galaxy light shading.
Error:
Dk=0.02
(1-contour)
(Gray & Taylor, et al., 2002, ApJ, 568,141)
11/15/2018
IDM2004, September, Edinburgh

10. Mapping the Dark Matter in 3-D
The lens potential, f, is a radial integral over the 3-D
Newtonian potential, F:
Observer
Galaxy clusters/lenses
Background source
11/15/2018
IDM2004, September, Edinburgh

11. 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
Galaxy clusters/lenses
Background source
11/15/2018
IDM2004, September, Edinburgh

12. Is 3-D dark matter mapping practical?
Shot-noise for 3-D dark matter potential map:
So Wiener filter in redshift:
Can now resolve clusters.
3-D lensing quality data already exists...COMB0-17 has 17 band photometric redshifts with Dz=0.01.
(Bacon & Taylor MN 2003; Taylor, et al MN 2004)
(Bacon & Taylor, 2003; Hu & Keeton, 2002)
11/15/2018
IDM2004, September, Edinburgh

13. The 3-D dark matter potential field
Galaxy density: z
1.0
0.8
A901a
A901b
A902
A901a
A901b
A902
CB1
0.6
0.4
Cosmic Web – bottom up scenario – clusters then filaments then walls (membranes).
Note that filaments not well traced by galaxies & too ephemeral to emit x-rays, so lensing only way to detect. Y X
(2-s threshold)
11/15/2018
IDM2004, September, Edinburgh
Taylor, et al, 2004 MN, in press

14. The 3-D dark matter potential and galaxy number density fields
Potential Field:
Galaxy number density:
Cosmic Web – bottom up scenario – clusters then filaments then walls (membranes).
Note that filaments not well traced by galaxies & too ephemeral to emit x-rays, so lensing only way to detect.
11/15/2018
IDM2004, September, Edinburgh
Taylor, et al, 2004 MN, in press

15. A901/2 + CB1 Cluster parameters
Cluster Redshift M (<0.5Mpc) L(<0.5Mpc) M/L
(1013Msun) (1011Lsun) (Msun/Lsun)
A901a
A901b A CB
Estimate projection-free masses of all objects.
Erratic mass-to-light ratio – non-equilibrium system.
Modelling with analytic and numerical methods.
(Taylor, et al, 2004 MN, in press)
11/15/2018
IDM2004, September, Edinburgh

16. IDM2004, September, Edinburgh
Cosmic Shear
Lensing by the large-scale dark matter distribution.
First detected by 4 groups in 2000.
11/15/2018
IDM2004, September, Edinburgh

17. Four random fields in COMBO-17 survey
2-D Dark Matter Maps:
Area = 1 sq deg.
Depth: z = 0.8.
Scale: 10 Mpc/h.
Chandra Deep Field
South Galactic Pole
S11
FDF
11/15/2018
IDM2004, September, Edinburgh

18. Cosmic Shear Power Spectrum
Maximum Likelihood Analysis of Cosmic Shear.
Measured over 4 random COMBO-17 fields.
R(Mpc/h)
zm = 0.85+/-0.05
from photometric
redshifts
(signal)
(noise)
Shear
Amplitude
Standard LCDM model
Multipoles
Brown, Taylor, et al,
2003, MNRAS, 341, 100
11/15/2018
IDM2004, September, Edinburgh

19. Results from Cosmic Shear
Combine with 2dF Galaxy Redshift Survey & pre-WMAP CMB Wm s8
CMB
2dF GL
s8(Wm/0.3)0.49=0.71+/-0.09
Lewis & Bridle (2002)
Percival et al (2002)
s8 = 0.73+/-0.05
Wm = 0.27+/-0.02
WMAP
(h=0.72, t=0.1)
Brown, Taylor, et al,
2003, MNRAS, 341, 100
11/15/2018
IDM2004, September, Edinburgh

20. IDM2004, September, Edinburgh
3-D Cosmic Shear
Shear probes the density field at different redshifts:
Cosmology
Shear-shear
cross-power
Observer
Redshift
11/15/2018
IDM2004, September, Edinburgh

21. The Growth of Dark Matter Clustering
Evolution of the matter power spectrum:
1-sigma
Pm(k,z)
c2-fit to data.
First detection of evolution of
Dark matter clustering.
A fundamental prediction of
Cosmology.
2-sigma
LCDM
Redshift
11/15/2018
IDM2004, September, Edinburgh
(Bacon & Taylor, et al 2004, MN)

22. Geometric test of Dark Energy
(Bhuvnesh Jain & AT, 2003, Phys Rev Lett, 91,1302)
Depends only on WV, w = p/r (and Wm+WK).
Observer
Galaxy cluster/lens z1 zL z2
11/15/2018
IDM2004, September, Edinburgh

23. Geometric test of Dark Energy
Estimate parameters by minimising c2 -fit over all source configurations.
Observer
Galaxy cluster/lens z1 zL z2
11/15/2018
IDM2004, September, Edinburgh

24. Geometric test of Dark Energy
(with Tom Kitching and David Bacon)
Geometric test applied to A901/2 clusters.
Dw~0.8 from 3 clusters.
Uncertainty scales as:
~1% for darkCAM on VISTA. WV w
A901/2
WMAP
Cosmic Web – bottom up scenario – clusters then filaments then walls (membranes).
Note that filaments not well traced by galaxies & too ephemeral to emit x-rays, so lensing only way to detect.
11/15/2018
IDM2004, September, Edinburgh

25. Measuring the evolution of Dark Energy
Measure Wv and w(a)=w0+wa(1-a).
Estimate error for SNAP (zm=1.5).
10% of sky: Dw=~1%, Dwa=~10%
wa=0 w0 wa w0 WV
11/15/2018
IDM2004, September, Edinburgh
Jain & Taylor, PhysRevLett, 2003

26. darkCAM on VISTA (area x fov) and timescales:
Comparison of lensing telescopes grasp
(area x fov) and timescales:
VISTA
(Visible & Infrared Survey
Telescope for Astronomy)
darkCAM
Proposal to PPARC to start in 2009.
(PI: Taylor)
w to ~1% accuracy.
3-D dark matter map of sky.
11/15/2018
IDM2004, September, Edinburgh

27. IDM2004, September, Edinburgh
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 darkCAM on VISTA.
11/15/2018
IDM2004, September, Edinburgh