A History of Shear Measurement Sarah Bridle, UCL

A History of Shear MeasurementSarah Bridle, UCL • The shear measurement problem • Status in 2004 • Quadrupole moments, Shapelets • (See later talk on KSB) • Past shear measurement challenges • STEP1, STEP2, STEP3, STEP4/GREAT08 • Winning methods from GREAT08 • Lensfit, Stacking • (See talks on gfit, KSB, post-GREAT08 methods)

Why do shear measurement? Galaxy clustering Supernovae Gravitational shear Quality of dark energy constraint Example for optical ground-based surveys Dark Energy Task Force report astro-ph/0609591 Gravitational shear has the greatest potential Big uncertainty largely due to shear measurement techniques

Definition of shear measurement Figure from the GREAT08 Handbook

PSF estimation and interpolation - less frequently discussed Shear measurement from known PSF - focus of this talk Figure from the GREAT10 Handbook

PSF measurement is very important Shear variance PSF ellipticity (Galaxy size / PSF size)4 Uncertainty on PSF size Uncertainty on PSF ellipticity • Need small round PSF • Need stable PSF A quadrupole-moment based example from Paulin-Henriksson, Amara, Voigt, Refregier, Bridle 2008

Galaxy Shear Measurement Family Tree in 2004 In person In paper Some advice Inspired by Tyson Valdes Wenk Bonnet Mellier Bertin Arnouts Smail et al Brainerd et al Kaiser, Squires, Broadhurst Kaiser, Luppino Rhodes Refregier Groth Erben Van Waerbeke Clowe Hoekstra Kaiser 2000 Schrabback Kleinheinrich Hammerele Miralles Bacon Marshall Gray Heymans Refregier Bacon Massey Bernstein Jarvis Kuijken Dahle Massey Brown Chang Refregier Bridle Gull Kneib Bardeau Hirata Seljak Heymans Miller Kuijken Moller Fabrice Simple model fitting Based on quadrupole moments Shapelets

Quadrupole moments: the simplest possible shear measurement method

Ellipticity definitions (i) i So ϵli can be treated as a noisy estimate of gi e.g. see Bartelmann & Schneider 1999 review p59+, Bonnet & Mellier 1995, Seitz & Schneider 1997 See relation to quadrupole moments e.g. in GREAT08 Handbook Appendix B

Ellipticity definitions (ii) i Shear responsivity Depends on properties of galaxies e.g. see Bartelmann & Schneider 1999 review p59+, Schneider & Seitz 1995 See relation to quadrupole moments e.g. in GREAT08 Handbook Appendix B

Shapelets • Laguerre polynomials • Polynomial times Gaussian • Nice QM formalism • Lensing distortion has simple effect • PSF convolution can be removed by matrix multiplication Massey & Refregier 2004

Shapelets • Three main approaches • Bernstein, Nakajima, Jarvis • Shear “circular” shapelet model to match the image • Refregier, Bacon, Massey • Use shapelet model to make perfect image. Measure Qij from this • Kuijken • Shear exactly circular shapelet model to match image Massey & Refregier 2004

Shapelets • Pros: • - Compact basis set • - Shearing and convolution v fast • Cons: • - QM formalism blindingly seductive? • Gaussian envelope not well matched to galaxies or psf. • See Sechlets(Kuijken), Sersiclets (Ngan, van Waerbeke et al 2009).. • - See Melchior et al 2009 Three main approaches • Bernstein, Nakajima, Jarvis • Shear “circular” shapelet model to match the image • Refregier, Bacon, Massey • Use shapelet model to make perfect image. Measure Qij from this • Kuijken • Shear exactly circular shapelet model to match image

Shear TEsting Programme (STEP) • Started July 2004 • Is the shear estimation problem solved or not? • Series of international blind competitions • Start with simple simulated data (STEP1) • Make simulations increasingly realistic • Real data

STEP1

m -20% 20% STEP1 Results → Existing results are reliable The future requires 0.0003 Heymans et al 2005 -0.2 0.2

STEP2 Massey et al 2007

STEP2 Results Massey et al 2007

Classification of methods in STEP2 Massey et al 2007

STEP cont’d • STEP3 • SpaceSTEP • Schrabback, Rhodes, Heymans • Very complicated PSFs, same galaxy/PSF size as STEP1, STEP2 – too hard? • STEP4 • Kuijken et al • Back to basics approach to dissect problems • Decision to set to wider community • So code and models used for …

GREAT08 Data

The Leaderboard at the GREAT08 Challenge Deadline

GREAT08 Results in Detail Bridle et al 2010

Classification of methods in GREAT08 Bridle et al 2010

Model fitting methods • Sheared shapelets • Nakajima & Bernstein; Kuijken • Sums of co-elliptical Gaussians • im2shape; Voigt & SB 2009 • Exponential or de Vaucouleurs profiles • Lensfit • gfit • im3shape • Arbitrary radial profile • Irwin & Shmakova 2005

LensFitMiller, Kitching, Heymans, Heavens, van Waerbeke 2007Kitching, Miller, Heymans, van Waerbeke, Heavens 2008 • Best usable method from GREAT08 by margin • Forward fit sum of exponential and de Vaucoulers profiles • Bayesian: Calculates mean of posterior ellipticity distribution • Modulated by shear sensitivity

Stacking Methods • Kuijken 1999 • Lewis 2010 (2nd in GREAT08) • Hosseini, Bethge 2010 (GREAT08 winner) Figure from GREAT08 Results paper

Kitching et al 2010

The Future JDEM HSC

My questions for GREAT10 results • Have we solved the galaxy challenge problem at the level of Stage III surveys yet? • Are some methods relatively insensitive to • Galaxy model (how much do we need to find out?) • PSF (how good do images need to be?) • Galaxy size (how small can we go?) • S/N (how low can we go?) • What are the most promising methods for practical PSF estimation?

A History of Shear Measurement Sarah Bridle, UCL