STEP: THE SHEAR TESTING PROGRAMME Konrad Kuijken Leiden

Gravitational shear Gradient of deflection  coherent distortions of galaxy shapes e1=e cos(2 PA) e2=e sin(2 PA)

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

Growth of structure Subtle tracer of expansion history

Lensing vs distance Lens bending angle depends on distance Integral measurement of mass distribution along sightline  =  (Dls / Ds) Tomography needed

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

Averaging ellipticities Shear = ell. of intrinsically round galaxy Response of ellipticity to shear depends on ellipticity Extreme example: e1=1  e1=1 under any 1 ‘Ring response’ e2 e1

Measuring galaxy ellipticity Intrinsic shape is altered by Lensing shear PSF smearing Pixellation (=boxcar smoothing+subsampling) Noise Some of the information loss irretrievable Sub-pixel information Photon noise

<x2>, <xy>, <y2> Ideally… Measure 2nd moments of light distribution <x2>, <xy>, <y2> Subtract PSF 2nd moments Form ellipticity (Ixx-Iyy, 2Ixy) Alas…

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

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)

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 =   =

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

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) Disk+bulge models (Mandelbaum et al)

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!

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.

Shapelets PRO: CON 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!

Sech-shapelets Gaussian  poly Sech  poly (radial orders 0,2,4,6,8,10)

Many methods! Shear PSF corr. Moments Model Subtract KSB B&J Shapelets Im2shape

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

STEP 1 Heymans et al 2005 CFHT-like simulations (single colour) Task: 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

(CFHT + coma, astigm., defocus, m=3, m=4) STEP1: Results 6 different PSF types (CFHT + coma, astigm., defocus, m=3, m=4) 5 sets of images, shears 1=0, 0.005, 0.01, 0.05, 0.1 Quantify results as out = (1+m) in + c

STEP1: Results ~7% calibration bias Good PSF anisotropy correction

STEP1: Results Some unexplained trends with magnitude Noise effect? Driven by size-mag relation in simulation? Polarizability error (Kaiser flow)?

STEP2 Massey et al 2006 More complex galaxies More complex PSF 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) )

STEP2: Results All improved! 1-2% calibration errors

STEP3 Space-like PSFs Results under analysis. Investigate subsampling (pixel size) Very non-Gaussian PSFs (ACS & SNAP - like) Results under analysis.

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

STEPWEB http://www.physics.ubc.ca/~heymans/step.html

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

2nd order light bending Failure of single lens plane approx. Eg singular isothermal sphere 1st order: 2nd order: accel. bigger by [1+O()] At most 10-3 effect, usually much smaller ~  b/2 b  c

Multiple lens planes 2 deflections at different z: ~1arcsec ~5kpc ~1Gpc

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) ?