Download - Cosmology with Gravitaional Lensing
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Cosmology with Gravitaional Lensing
Bhuvnesh Jain
University of Pennsylvania
• Current measurements in weak lensing
• New techniques for probing dark energy
• Dark matter/dark energy with cluster arcs
• What advances are needed?
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Collaborators
Gary Bernstein
Mike Jarvis
Masahiro Takada
Andy Taylor (Edinburgh)
Wayne Hu (Chicago)
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Galaxy Redshift Survey
Gravitational Lensing
CMB
Measure correlation statistics Constraints on cosmological models
Cosmological Surveys
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Cosmology: Length and time scales
• CMB: z ~ 1100 d > 50 Mpc
• Galaxy Surveys: z < 0.3 d < 200 Mpc
• Lyman-alpha: z ~ 2 d < 40 Mpc
• Galaxy clusters: z < 1 d ~ 10 Mpc
• Weak lensing: z < 0.4 d < 20 Mpc
Lensing 2006: z < 0.6 d < 100 Mpc Lensing 2013: z < 1 0.02 < d < 500 Mpc
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Convergence & Shear due to Lensing
• Image distortion can be linearly decomposed into convergence and shear .
• and are given by the projected gravitational potential:
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≡12 ∂1
2 + ∂22
( )ϕ 2−d = Ωm dz W (z,zs)δ∫ (z)
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1 ≡ 12 ∂1
2 −∂22
( )ϕ 2−d ,
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2 ≡ ∂1∂2ϕ 2−d
• 1 and 2 give the ellipticity induced on a galaxy image.
• , ~ O (1%) for typical line of sight!
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W (z,zs)∝dLS(z,zs)dL(z)
dS(zs)is the geometric factor
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Simulated Lensing Maps
Field size: 3 x 3 deg, RMS amplitude: 2%
Jain, Seljak & White 2000
ShearConvergence
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2-Point Correlation Function
x
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x + r
Lensing correlations given by projection of the mass power spectrum:€
ξ(r) = f (x) f (x + r) ⇔F .T .
P(k)
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(θ) = dz W 2(z)∫ dk∫ P(k,z) F(k,θ,z)
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Measurement of cosmic shear
Intrinsic ellipticity of source galaxies > 10 x lensing signal (). Smooth over patches of sky to measure mean shear.
θ
Same argument applies to shear 2-point correlations.
Noise contribution to is plus sample variance.
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obs
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jasdkf
Average its square over
patches shear variance
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σ2
Npair
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Lensing measurements
• Weak lensing in “blank fields” detected in 2000
• Shear correlations measured over 1 arcmin - 1 deg
• Constrain mass power spectrum and mean mass density
• Errors on measured parameters: ~10% currently.
• Prospects: effective survey size will increase 10-fold in 3 years, and about 1000-fold in 10 years.
• Goal: Better than 1% accuracy in lensing measurements.
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Shear Variance Measurements
Aperture Mass Shear Variance
Jarvis et al 2002
Reanalysis of psf fitting (M. Jarvis): lower B-mode. New result: σ8=0.85 +/- 0.1. Other groups have new analyses as well.
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E/B mode decomposition
E mode B mode
Gravitational lensing due to scalar potential field: no B-mode
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Cosmological Mass Power Spectrum
“Vanilla” Lambda-CDM model (Tegmark & Zaldarriaga 2002)
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Wide field lensing surveys
• Deep Lens Survey, s=30 deg2, ng=50 arcmin-2, 4 filters
• CFH Legacy Surveys=200 deg2, ng=30 arcmin-2, 5 filters
• LSST (Large Synoptic Survey Telescope)– 8.2 m, Field of view: 7 deg2
– s=4000 deg2, ng=50 arcmin-2, 5 filters
• SNAP (Supernova/Acceleration Probe)– 2m, Field of view: 1 deg2
s=1000 ? deg2, ng=100 arcmin-2, 9 filters
• PANSTARRS, VST…
Future surveys
Ongoing surveys
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Tomography, cosmography, power, bispectra..
Mean tangential shear inside aperture compared for source galaxies at different z.
measured at different z.
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(θ)
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Lensing tomography
Shear at z1 and z2 given by integral of growth function &
distances over lensing mass distribution.
z1
z2
zl1
lensing mass
zl2
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Sensitivity to dark energy
Lensing fields depend on: Distances affect W , sinceGrowth rate affects Both depend on integrals of expansion rate:
Lensing tomography probes dark energy equation of state. Empirical approach:
de = de/critical : dark energy density
P = w(a) de : equation of state
w(a) = w0 + wa(1-a)a = 1/(1+z) - expansion scale factor
w0 is constant term, wa the time evolution term
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=m dz W (z,zs)δ∫ (z)
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H ≡a.
a∝ ρ
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W ∝ d(z,zs)d(z) /d(zs)
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1l
3l
1l2l
3l
Tomography: power spectrum and bispectrum
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( i)κ ( j ) ⇒ C(ij )(l) α W 2δ 2
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( i)κ ( j )κ (k ) ⇒ B(ijk )(l1,l2,l3) α W 3δ 4 : a function of triangles
: a function of separation l
2l€
l
€
z1
€
z2
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Lensing power spectrum
The theorists version of a future lensing measurement
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All triangle configurations, auto- and cross-spectra used. l < 3000 or > 5’.
Using CMB priors improves constraints on w0 and wa by over a factor of 2. (2-point: Hu 99,02; Huterer 02; Heavens 03; Linder,Jenkins 03; Song,Knox 03)
Parameter forecasts with tomography
Takada & Jain 03
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Lensing tomography: Take II
What good are the foreground galaxies?
z1
z2
zl1
lensing mass
zl2
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Cross-correlation cosmography
Galaxy-shear cross correlation, or mean tangential shear:
Ratio with 2 background redshift slices:
Relative shear amplitude is a pure geometric quantity!Stack groups and clusters: compare shear amplitudes in apertures ~ arcminute with varying background redshift. (Jain & Taylor 03) (Bernstein, Jain 03; Song, Knox 03; Zhang, Hui, Stebbins 03; Hu, Jain 03)
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Shear in apertures
• Estimate geometric factor for each aperture• Combine estimates to probe dark energy evolution
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Joint galaxy-lensing analysis
fsky =0.1; ng=70 survey
• Ongoing/future surveys: joint measurement of galaxy clustering and lensing
• 1st step: use all 2-point correlations and cross-correlations (Hu & Jain 03).
• Multiple probes of dark energy from single unified analysis
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HST and weak lensing
- Dark energy with lensing: Small effects, sensitive to biases in
photo-z’s or PSF anisotropy
- Open questions: strategy for future space and ground surveys?
- HST: Deep multicolor images, with ~0.1 arcsec resolution
- Can make galaxy samples, as a function of type and z, up to z~2-3
Multi-color COSMOS would be great (for both ground and space plans)!
- ACS TNO deep field (Bernstein et al) valuable sample for SNAP planning
- Ongoing work on relating galaxy properties with ambient mass structures
- 3D mass mapping needs deep multicolor, high-res imaging!
- Using size magnification as an entirely independent lensing measure
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Simulated cluster with arcs at z=1,2,3 (Meneghetti et al 2004) See: Soucail, Kneib, Golse 04 for observational attempt!
Cosmography with cluster arcs
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Cosmography with cluster arcs
Critical curves for z=1,2 Average critical curve size vs. z
Sample of ~20 simulated lens clusters in 5 models. Results preliminary!
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Constraints on w and Cluster Mass
With a Golden Lens can get mass and w from a single cluster.Helpful factors: Velocity Dispersions, SZ, X-ray, Luck…Statistical alternative: compare ~100 observed/simulated clusters
No external info. Arc zs=1,2 Vel. Dispersion + Arc zs=1,2,3
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Gravitational Telescopes
Arcs at z~7 and z~10!Magnification: x20 to x50.
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Cluster arcs and dark matter
• Radial and tangential arcs probe inner mass profiles
• With vel dispersions, attempt robust measurement of mass profile
• Compare to NFW predictions constrain dark matter properties
Sand et al 2002, 2003
• Sensitivity to ellipticity and substructure in the mass distribution?
Bartelmann & Meneghetti; Dalal & Keeton
• Gravitational telescopes: galaxy samples approaching z~10
• Arcs at multiple redshifts probe of dark energy
Questions about techniques remain, but real potential for discovery!
Observe tens of clusters at high resolution, with X-ray and spectroscopy
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Summary
• Lensing tomography probes dark energy using the evolution of clustering and distances factors
• Lensing cosmography: a geometric probe of dark energy
• Arcs in galaxy clusters: dark matter/dark energy
• HST: cluster arcs, and planning weak lensing surveys.