STEP: THE SHEAR TESTING PROGRAMME

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STEPTHE SHEAR TESTING PROGRAMME

• Konrad Kuijken
• Leiden

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Gravitational shear

• Gradient of deflection ? coherent distortions of
  galaxy shapes

e1e cos(2 PA) e2e sin(2 PA)
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Accurate shear measurements

• Weak lensing measures
• Power spectrum
• Cluster abundance
• Light-mass correlation
• Why precision?
• Trace growth of structure (cosmology probe)
• Dark matter/galaxy connection
• Halo shapes

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Growth of structure

• Subtle tracer of expansion history

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Lensing vs distance

• Lens bending angle depends on distance
• Integral measurement of mass distribution along
  sightline
• ?? ? (Dls / Ds)
• Tomography needed

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Requirements

• High fidelity shear measurement
• Well-controlled distance measurements (understand
  errors in redshifts)
• Accurate predictions of power spectrum
• Matter power spectrum
• Consequent shear power spectrum

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Measuring shear

• Galaxies randomly oriented
• Shear introduces a bias in orientation and
  ellipticity
• Try to detect the observed shape of intrinsically
  round galaxy

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Averaging ellipticities

• Shear ell. of intrinsically round galaxy
• Response of ellipticity to shear depends on
  ellipticity
• Extreme example e11 ? e11 under any ?1
• Ring response

e2
e1
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Measuring galaxy ellipticity

• Intrinsic shape is altered by
• Lensing shear
• PSF smearing
• Pixellation (boxcar smoothingsubsampling)
• Noise
• Some of the information loss irretrievable
• Sub-pixel information
• Photon noise

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Ideally

• Measure 2nd moments of light distribution
• ltx2gt, ltxygt, lty2gt
• Subtract PSF 2nd moments
• Form ellipticity
• (Ixx-Iyy, 2Ixy)
• Alas

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Techniques

• Ellipticity from
• Weighted 2nd moments
• Model fitting
• PSF / pixellation correction from
• Model fitting of PSF effect
• Weighted 2nd moments
• Pre-smoothing images with kernel

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Kaiser, Squires, Broadhurst 95

• Weighted 2nd moments
• Gaussian wt. function
• PSF correction 2 stages
• PSF anisotropy correction
• Assumes anisotropic part of PSF is compact
• Polarizability depends on 4th weighted moments
• PSF circularization correction (LK97)
• Very succesful, but imperfect
• Very good for Gaussian PSF

? dx dy x2 W(r) I(x,y)
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KSB PSF model

• Compact anisotropic core ? circular PSF
• Gaussian OK
• (separable in x,y)
• Moffat func not OK
• Radial PSF profile implicitly determines
  ellipticity profile

?

?
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The weight function
Hoekstra et al. 1998
KSB formalism works for any Gaussian wt.
function. Pick one that is optimal for S/N

• Radius of PSF weight function matters if
  ellipticity of PSF depends on radius
• Empirically, best results for radius that matches
  galaxy

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Direct modelling

• Model sources as full PSF ? elliptical model
• Read off ellipticity
• Different galaxy models
• Multiple elliptical Gaussians (KK99, Bridle
  Im2shape)
• Shapelets series (Refregier et al, Massey et al,
  KK06)
• Sheared shapelets (Bernstein Jarvis)
• Diskbulge models (Mandelbaum et al)

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Stacking

• Average galaxy is intrinsically round
• Stack observed sources
• Write as sheared round source ? PSF
• Characterized by single ellipticity and radial
  brightness profile
• Subtlety centroid errors
• Extra smearing term. Not necessarily isotropic!

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Shapelets

• Direct modelling of PSF and sources as Gaussians
  x polynomials (QHO!)
• Ellipticity measurement and PSF effects analytic
• Model a galaxy as
• PSF ? 1?1 S1?2 S2 ? C
• All operations linear, matrix multiplications of
  shapelet coefficients.

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Shapelets

• PRO
• Shapelet coeffs replace pixels (compression)
• Error propagation simple
• Simple combinations of coeffs. mimic weighted
  moments
• Can be extended to flexions
• CON
• Galaxies are not Gaussian!

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Sech-shapelets
Gaussian ? poly
Sech ? poly
(radial orders 0,2,4,6,8,10)
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Many methods!
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STEP

• Confront all methods and software with uniform
  datasets
• Large enough to draw significant conclusions on
  accuracy
• Blind simulations
• Involve most of the community
• Meet regularly to discuss progress

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STEP 1Heymans et al 2005

• CFHT-like simulations (single colour)
• Skymaker, Van Waerbeke
• Galaxies exp. disk de Vauc bulge
• Random orientations, axis ratio distribution
• Stars added into the images
• 100,000 galaxies per PSF/shear set (30 sets)
• Task
• Model PSF
• Deduce average shear in the images
• End-to-end pipeline tests

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STEP1 Results

• 6 different PSF types
• (CFHT coma, astigm., defocus, m3, m4)
• 5 sets of images, shears
• ?10, 0.005, 0.01, 0.05, 0.1
• Quantify results as
• ?out (1m) ?in c

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STEP1 Results

• 7 calibration bias
• Good PSF anisotropy correction

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STEP1 Results

• Some unexplained trends with magnitude
• Noise effect?
• Driven by size-mag relation in simulation?
• Polarizability error (Kaiser flow)?

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STEP2Massey et al 2006

• More complex galaxies
• Shapelet reconstructions
• Evolving galaxy pop
• More complex PSF
• suppress shape noise artificially
• Include each galaxy with 2 PA, 90 deg apart (i.e.
  at (e1,e2) and (-e1,-e2) )

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STEP2 Results

• All improved! 1-2 calibration errors

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STEP3

• Space-like PSFs
• Investigate subsampling (pixel size)
• Very non-Gaussian PSFs (ACS SNAP - like)
• Results under analysis.

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STEP4

• Back to Basics
• Take out effects of
• Source detection
• Source overlap
• Star/galaxy separation
• FWHM 1.4 (gals), 0.7 (PSF), 0.2 pixels
• Simulations of grids of galaxies, 32 different
  shears, enough galaxies to get statistical error
  on measured m, c parameters down to 0.001
• Blind analysis

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STEPWEB

• http//www.physics.ubc.ca/heymans/step.html

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Outstanding issues

• Colour effects
• PSF SED different from galaxies
• Ellipticity-dependent selection bias
• Pixel noise correlations
• Non-linear shear effects?
• 2nd order light bending

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2nd order light bending

• Failure of single lens plane approx.
• Eg singular isothermal sphere
• 1st order
• 2nd order accel. bigger by 1O(?)
• At most 10-3 effect, usually much smaller

? b/2
b
? c
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Multiple lens planes

• 2 deflections at different z

1arcsec
5kpc
1Gpc
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Further steps ( STEPs)

• Key issues
• Modelling PSF accurately, including interpolation
• Source selection independent of intrinsic
  ellipticity
• Propagating errors covariances
• PSF Gaussianization KSB how far will it get
  you?
• Photo-z accuracy experiment (PACE) ?