The next decade of
weak lensing science
Rachel Mandelbaum, CMU
Cosmology
 A homogeneous and isotropic universe
 Spatially flat and expanding (accelerating!)
 General Relativity:
Function of the
metric (defining
space-time behavior)
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Stress-energy
tensor describes
matter/energy
contents
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?????
Name for
model:
CDM
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??
Picture credits: NASA/WMAP science team
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Quantum fluctuations
seed small (/ ~10-5)
inhomogeneities…
…which are imprinted
in CMB...
Matter domination:
growth through
gravitational instability
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Picture credits: NASA/WMAP science team
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Two classes of cosmological probes
Geometric: SN1A, BAO
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Growth of structure
Picture credits: ESA/ESO (left), MPE/V. Springel (right)
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Summary: current status in cosmology
 An observationally supported big picture
 BUT… many fundamental uncertainties
 nature of DM and DE,
 nature of inflationary era,
 GR confirmation on many scales.
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A key problem:
 The universe is dominated by dark contents.
 But…we cannot directly observe those contents
using a telescope.
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Gravitational lensing
Lensing deflection of light:
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Sensitive to all matter
along line of sight,
including dark matter!
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Weak lensing
Unlensed
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Lensed
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Galaxies aren’t really round
NASA, ESA, S. Beckwith (STScI) and the HUDF Team
Cosmic shear
Shape autocorrelation statistical map of large-scale structure
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Galaxy-galaxy lensing
 Stacked lens galaxy position – source galaxy
shape cross-correlation
 Reveals total average matter distribution around
lens galaxies or cluster (galaxy-mass correlation)
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State of the field of weak lensing
mid-1990s: first detections of weak lensing
2000-2001: first cosmological weak lensing measurements (~20-30%
errors)
2002-2012: increasingly precise lensing measurements in a variety of
datasets, down to ~5-10% errors
2013: several large, ground-based surveys will start measuring
lensing with unprecedented precision (~2%)
~2020: 2 surveys will start to measure lensing with sub-% precision
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Subaru telescope
 8.2 meter primary mirror
 Mauna Kea
 Excellent imaging
conditions
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Subaru telescope
 Many instruments for optical and spectroscopic observations,
e.g. Suprime-Cam
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Miyatake, Takada, RM, et al (2012)
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Picture credit: S. Miyazaki
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HSC is on the telescope!
HSC blog at naoj.org
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Looking good!
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3-layer HSC survey
 Wide: ~1400 deg2, i<25.8 (grizy)
 Weak lensing, z<1.5 galaxy populations
 Deep: ~26 deg2, 1 mag deeper, 5 wide+3 NB filters
 Ly-α emitters, quasars, deeper galaxy populations, lensing
systematics, …
 Ultradeep: 3 deg2, 1 mag deeper, 5 wide+6 NB filters
 Supernovae, galaxies to z<7
 Important synergies: CMB (ACT+ACTPol), redshifts (BOSS
+ assorted other), NIR, u band, …
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What has driven this
development?
 ~8-10 years ago, people started to realize how very
powerful cosmic shear is as a probe of dark energy!
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(LSST science book)
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What has driven this
development?
 ~8-10 years ago, people started to realize how very
powerful cosmic shear is as a probe of dark energy!
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Zhan et al. (2006, 2008)
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A reminder
 Cosmic shear measures the matter power spectrum
 This is easily predicted from theory (modulo small-scale
effects)
 Contrast: the galaxy power spectrum from redshift
surveys – galaxies are a biased tracer of matter
Galaxies
Dark matter halo
Density
Position
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BUT
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This is actually kind of difficult.
Cosmic shear is an auto-correlation of shapes:
Multiplicative biases are an issue!
Coherent additive biases become an additional term!
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That’s not the only problem, either.
 Intrinsic alignments
 Theoretical uncertainties on small scales (e.g.
baryonic effects)
 Photometric redshift uncertainties
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Implications
 As datasets grow, our control of systematics must get
increasingly better
 The past ~3 years have seen a change of perspective
within the lensing community:
 We should measure cosmic shear
 But we should also identify combinations of lensing
measurements with other measurements that allow us to
calibrate out / marginalize over systematics directly
 Use ALL the information available
 Minimize the combination of statistical + systematic error!
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What data will we have?
 The lensing shear field: HSC
 The 2d galaxy density field: HSC
 (Sometimes) 3d galaxy density field and velocity field,
(M. White)
with spectroscopy: BOSS
 X-ray (galaxy clusters): XMM
 SZ (galaxy clusters), CMB
lensing: ACT
 Lensing magnification field?
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Summary of approach
to future data:
Cross-correlate
everything with
everything
= more information
= less sensitivity to observational uncertainties
specific to one particular method
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What about galaxy-galaxy
lensing?
 Typically undervalued for cosmology, because it measures
gm correlations, not mm
 Observationally easier:
 Coherent additive shear errors do not contribute at all!
(cross-correlation)
 Intrinsic alignments:
 Don’t enter at all, with robust lens-source separation
 If sources are not well behind lenses, they contribute, but in a
different way from cosmic shear
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Observational quantities
•  gg from galaxy clustering
•   gm from g-g weak lensing
• Infer matter clustering (schematically):
Constrain
nonlinear matter
power spectrum
on large scales
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Let’s include cosmic shear
 Use cosmic shear (mm), galaxy-galaxy lensing (gm), and
galaxy clustering (gg)
 Dependence on intrinsic alignments, shear systematics:
 Different for the two lensing measurements
  Joachimi & Bridle 2011, Kirk et al. (2011), Laszlo et al.
(2011) showed that the cosmological power is = that of
cosmic shear, even when marginalizing over extensive
models for systematics!
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A concrete example:
Lensing + clustering in SDSS DR7
(RM, Anze Slosar, Tobias Baldauf, Uros
Seljak, Christopher Hirata, Reiko
Nakajima, Reinabelle Reyes, 2012)
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Observational quantities
•  gg from galaxy clustering
•   gm from g-g weak lensing
• Infer matter clustering (schematically):
Constrain
nonlinear matter
power spectrum
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Cross-correlation
coefficient between
galaxies, matter
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Problem: small scales
Theoretical uncertainties in Σ (surface density):
 Baryonic effects
 Cross-correlation ≠ 1
 Cannot remove by avoiding small scale ΔΣ
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Integration lower
limit is the problem
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Solution to small-scale issues
• Define “Annular differential surface density”
(ADSD):
→0 at R0
→ΔΣ at R>>R0
NO dependence on signal below R0!
T. Baldauf, R. E. Smith, U. Seljak, RM, 2010, Phys. Rev. D, 81, 3531
RM, U. Seljak, T. Baldauf, R. E. Smith, 2010, MNRAS, 405, 2078
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Cross-correlation coeff (rcc)
Example from simulations
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Using ΔΣ
Reconstruction
Using ϒ, R0=3 Mpc/h
ϒmm
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Sensitivity to cosmology
Fiducial
cosmology:
Ωm=0.25
σ8=0.8
ns=1.0
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Results
 Lenses: SDSS-I spectroscopic samples:
 LRGs, z~0.3, typically 3L*, ~105
 Main, z~0.1, typically L*, 6 × 105
 Sources: 6 × 107 fainter galaxies
 Treat samples separately, for sanity checks
 Updated treatment of lensing systematics
(RM et al. 2011, Reyes et al. 2011)
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Example of current data
Stacked data:
~105 LRGs
(lenses),
70M sources
Lensing
signal
Transverse separation R (Mpc/h)
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Lensing data
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Clustering data
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Actual procedure
 Direct fitting:
 Nonlinear power spectrum
 PT-motivated
parametrization of nonlinear bias
 With these data alone,
fitting for σ8, Ωm, and bias,
marginalizing over bias and
lensing calibration:
 σ8 (Ωm/0.25)0.57 = 0.80±0.05
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Non-flat, free wde
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Comparison to cosmic shear results
 COSMOS (Schrabback et al. 2010), 11% σ8 constraint
 CFHTLenS (Kilbinger et al. 2012), 4% σ8 constraint
 Typical z~1, 0.8 vs. 0.25 for SDSS
 SDSS gives better control of redshift systematics
Results shown here establish SDSS
among the most competitive extant
surveys for weak lensing cosmology!
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Near future improvements
BOSS + HSC:
Less dominated by
lensing statistical
errors
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But that’s not all…
Small-scale lensing profiles reveal galaxy DM halos
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Transverse separation R (Mpc/h)
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Example of how we can use this: FoG
• Small-scale effect due to
velocity dispersion within
halos
• Cannot simply eliminate
by using only individual
halos, unless chosen
“center” is really at center
White et al. (2011): contours of
3d correlation function
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Idea for how to calibrate out FoG
 Hikage, Takada, Spergel (2011)
 Rely on spectroscopic / photometric survey synergy
 Select halos, then compare several measurements for
different choices of halo centers:
 Redshift-space power spectra
 Galaxy-galaxy lensing (matter distribution)
 Photometric galaxy cross-correlation
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Modeling
Hikage, RM, Takada,
Spergel (2012)
 Need HOD model for how galaxies populate halos
 Include variable fraction that are offset within halos, their
spatial and velocity distributions
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The punch line
 40% (70%) of bright
(faint) LRGs are actually
off-centered satellites
 Typical off-centering
radius of 400 kpc/h
 Typical velocity
dispersion: 500 km/s
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Conclusions
 Current g-g lensing measurements:
 Test theory predictions for galaxy-DM relationship
 Constrain cosmological parameters at various redshifts
 Lensing is the ONLY technique that directly probes
the total matter distribution!
 Future datasets: better S/N  cosmologically
interesting powerful constraints on growth of
structure, done optimally via combination of
multiple observables
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