The next decade of weak lensing science

Rachel Mandelbaum, CMU

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CosmologyA homogeneous and isotropic

universe

Spatially flat and expanding (accelerating!)

General Relativity:Function of the metric (defining space-time behavior)

Stress-energy tensor

describes matter/energy

contents

R. Mandelbaum 3Picture credits: NASA/WMAP science team

Name for model: CDM

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4Picture credits: NASA/WMAP science team

Quantum fluctuations seed small (/ ~10-5) inhomogeneities…

…which are imprinted in CMB...

Matter domination: growth through gravitational instabilityR. Mandelbaum

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Two classes of cosmological probes

Geometric: SN1A, BAO

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 uncertaintiesnature 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

Lensed

Galaxies aren’t really round

NASA, ESA, S. Beckwith (STScI) and the HUDF Team

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Cosmic shearShape autocorrelation statistical map of large-scale structure

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Galaxy-galaxy lensingStacked 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

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Subaru telescope

8.2 meter primary mirror

Mauna Kea

Excellent imaging conditions

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Subaru telescopeMany instruments for optical and spectroscopic

observations, e.g. Suprime-Cam

Miyatake, Takada, RM, et al (2012)

18Picture credit: S. MiyazakiR. Mandelbaum

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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!

(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!

Zhan et al. (2006, 2008)

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A reminderCosmic 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

Position

GalaxiesDensity

Dark matter halo

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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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ImplicationsAs 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, with spectroscopy: BOSS

X-ray (galaxy clusters): XMM

SZ (galaxy clusters), CMB

lensing: ACT

Lensing magnification field?

(M. White)

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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

• ξgg from galaxy clustering

• ρξgm 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

• ξgg from galaxy clustering

• ρξgm from g-g weak lensing

• Infer matter clustering (schematically): Constrain

nonlinear matter power spectrum

Cross-correlation coefficient between galaxies, matter

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Problem: small scalesTheoretical uncertainties in Σ (surface

density): Baryonic effects Cross-correlation ≠ 1 Cannot remove by avoiding small scale ΔΣ

Integration lower limit is the problem

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Solution to small-scale issues

• Define “Annular differential surface density” (ADSD):

NO dependence on signal below R0!

→0 at R0

→ΔΣ at R>>R0

T. Baldauf, R. E. Smith, U. Seljak, RM, 2010, Phys. Rev. D, 81, 3531RM, U. Seljak, T. Baldauf, R. E. Smith, 2010, MNRAS, 405, 2078

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Example from simulationsC

ross

-corr

ela

tion

coeff

(r c

c)

Using ΔΣ

Using ϒ, R0=3 Mpc/h

Reconstruction

ϒmm

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Sensitivity to cosmology

Fiducialcosmolog

y:

Ωm=0.25σ8=0.8ns=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 non-linear 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

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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ModelingNeed HOD model for how galaxies populate

halos

Include variable fraction that are offset within halos, their spatial and velocity distributions

Hikage, RM, Takada, Spergel (2012)

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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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ConclusionsCurrent 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