A Historical Review of Shear Measurement Sarah Bridle

1. A Historical Review of Shear MeasurementSarah Bridle • The shear measurement problem • Family tree in 2004 • Shear measurement challenges • STEP1, STEP2, STEP3, STEP4/GREAT08 • Summary of key methods today • KSB, Shapelets, Model fitting, FDNT, Stacking • (See entire talks coming next: Lensfit, HOLICS)

2. A Historical Review of Shear MeasurementSarah Bridle • The shear measurement problem • Family tree in 2004 • Shear measurement challenges • STEP1, STEP2, STEP3, STEP4/GREAT08 • Summary of key methods today • KSB, Shapelets, Model fitting, FDNT, Stacking • (See entire talks coming next: Lensfit, HOLICS)

3. Comparison of different methods 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

4. Definition of shear measurement Figure from the GREAT08 Handbook

5. Typical galaxy used for cosmic shear analysis Typical star Used for finding Convolution kernel

6. Typical Data

7. Accuracy requirements Amara, Refregier 2008 GREAT08 Q

8. Shear accuracy requirements 1000 40 300 Q~ Subaru KIDS Pan-STARRS Euclid LSST WFIRST CFHTLS DES 2005 06 07 08 09 10 11 12 13 14 15 16 17 18 19 2020 STEP1 STEP3/4 GREAT10 STEP2 GREAT08

9. A Historical Review of Shear MeasurementSarah Bridle • The shear measurement problem • Family tree in 2004 • Shear measurement challenges • STEP1, STEP2, STEP3, STEP4/GREAT08 • Summary of key methods today • KSB, Shapelets, Model fitting, FDNT, Stacking • (See entire talks coming next: Lensfit, HOLICS)

10. 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 Kuijken Moller Fabrice Bardeau Faure Cypriano Kneib

12. A Historical Review of Shear MeasurementSarah Bridle • The shear measurement problem • Family tree in 2004 • Shear measurement challenges • STEP1, STEP2, STEP3, STEP4/GREAT08 • Summary of key methods today • KSB, Shapelets, Model fitting, FDNT, Stacking • (See entire talks coming next: Lensfit, HOLICS)

13. 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

14. STEP1

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

16. STEP1 Results - Dirty laundry Measured minus true g Require 0.0003 0 Average -0.0010 -0.0050 Heymans et al 2005 High noise Low noise ~ noise level of image

17. STEP2 Massey et al 2007

18. STEP2 Results

19. 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 …

21. GREAT08 A computational challenge • Active leaderboard • 30 000 000 galaxy images • 200 GB data • 1 week to download to US • Typical methods – 1 second per galaxy > 1 year to run the code once

22. GREAT08 Data

23. The Leaderboard at the GREAT08 Challenge Deadline

25. GREAT08 Results in Detail Bridle et al 2010

26. Kitching et al 2010

27. A Historical Review of Shear MeasurementSarah Bridle • The shear measurement problem • Family tree in 2004 • Shear measurement challenges • STEP1, STEP2, STEP3, STEP4/GREAT08 • Summary of key methods today • KSB, Shapelets, Model fitting, FDNT, Stacking • (See entire talks coming next: Lensfit, HOLICS)

28. Summary of current key methods • KSB • Shapelets • Model fitting methods • FDNT • Stacking approaches See entire talks coming next on: • Lensfit • HOLICS

29. Quadrupole moments: the simplest possible shear measurement method

30. Effect of shear on quadrupole moments

31. Ellipticity |ϵ| = (a-b)/(a+b) from quadrupole moments Nasty noise properties Where 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

32. Ellipticity ||=(a2-b2)/(a2+b2)from quadrupole moments

33. Ellipticity ||=(a2-b2)/(a2+b2)from quadrupole moments Taylor expand and use Depends on properties of galaxies Shear responsivity e.g. see Bartelmann & Schneider 1999 review p59+, Schneider & Seitz 1995

34. KSB:As above, with weight function Herein lies significant complications The last two are the same in the case W(x,y)=1

35. Why do weighted quadrupole moments?

36. The KSB shear responsivity Kaiser, Squires & Broadhurst 1995, Luppino & Kaiser 1997, Hoekstra et al. 1998

37. DEIMOSMelchior, Viola, Schaffer, Bartelmann Weight function optimised per galaxy (cf Bernstein & Jarvis ellipto)

38. 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

39. 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

40. 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

41. Model fitting methods • Sheared shapelets • (Nakajima & Bernstein; Kuijken) • Sums of co-elliptical Gaussians • (SB et al 2001; Voigt & SB 2009; Zuntz, Kacprzak, Voigt, SB..) • Exponential or de Vaucouleurs profiles • Lensfit (see Lance’s talk) • gfit (Paulin, Gentile) • Arbitrary radial profile • (Irwin & Shmakova 2005)

42. Is there a bias on gwhen fit 1 elliptical Gaussian? Voigt & Bridle 2009

43. Modelling the galaxy with a single Gaussian: Gaussian PSF, small pixels Simulated galaxy True convolved image PSF = Gaussian Best-fit model Model = Gaussian PSF = true PSF Answer: Yes! - bias on galaxy ellipticity measured > 1% Need to model the galaxy with more than 1 Gaussian!

44. Is there a bias on gwhen fit 1 elliptical Gaussian? No No Yes No No Yes Voigt & Bridle 2009

45. Model galaxy as multiple co-elliptical Gaussians Residuals Model = Gaussian Simulated galaxy = exponential 1 G 2 G • Tied parameters: x0,y0,e,phi • Free parameters: a,A 3 G Voigt & Bridle 2009

46. Is there a bias on gwhen fit elliptical isophote model? Voigt & Bridle 2009

47. Is there a bias on gwhen fit elliptical isophote model? No No No No No Yes Voigt & Bridle 2009 See also Lewis 2010

48. Fourier Domain Null Test (FDNT)Bernstein 2010 + Correction factor differential shear based on properties of population

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

50. Conclusions • This problem is deceptively hard • Some people think we’re crazy for even trying • Billions of dollars might be spent relying on us • Challenges have been great • But see Catherine’s discussion • Many new ideas • Are there any completely fresh approaches?