1. Measuring Cosmic Shear Sarah Bridle Dept of Physics & Astronomy, UCL What is cosmic shear? Why is it hard to measure? The international competition Overview of conventional approaches Our approach

2. Gravitational Lensing  = 4 G M / (c 2 b) M b 

3. Extremely rare!

4. Distribution of matter - According to simulations - NB. is mostly dark

5. Cosmic Shear: Qualitative Tyson et al 2002 Massively exaggerated

6. Cosmic Shear: Quantitative Gravitational lensing by typical patches of Universe ~~ matrix distortion of each galaxy image –  / gravitating mass density –  i (x) = ∫  (x’) W i (x-x’) dA Cosmic shear:  ~ 0,  i ~ 0.01 –e.g. circular galaxy → ellipse with a/b ~ 1.01

7. What do we want to learn from cosmic shear? Distribution of dark matter And hence infer –Amount of dark matter –Clumpiness of universe after inflation –Amount of dark energy –Equation of state of the dark energy But is the current model right? –95 per cent of the Universe is a mystery –Dark energy does not make sense We hope to gain clues to help a new Einstein

8. Weak Lensing + CMB (approximate)

9. Deep optical images William Herschel Telescope La Palma, Canaries

11. Typical star Typical galaxy used for cosmic shear analysis

12. Saturated star Diffraction spikes Variable background Typical star Typical galaxy used for cosmic shear analysis

13. Why is this hard? Galaxies are not circles or ellipses Galaxy orientations may align during formation Telescope and atmosphere convolve image = point spread function (psf) –spatially varying –time varying CCD responsivity, cosmic rays, metors, unresolved sources, variable atmosphere, saturated stars Pixelisation of images (~sum of light over pixel) Partial and patchy sky coverage We don’t have galaxy distances Mass distribution is not Gaussian

14. Why is this hard? Galaxies are not circles or ellipses Galaxy orientations may align during formation Telescope and atmosphere convolve image = point spread function (psf) –spatially varying –time varying CCD responsivity, cosmic rays, metors, unresolved sources, variable atmosphere, saturated stars Pixelisation of images (~sum of light over pixel) Partial and patchy sky coverage We don’t have galaxy distances Mass distribution is not Gaussian

15. WHT Bacon, Refregier & Ellis 2000 Ellipticities of the non-saturated stars

16. WHT Bacon, Refregier & Ellis 2000 Ellipticities of the non-saturated stars

17. CTIO BTC Jarvis & Jain 2005

19. Conventional approach: Split into several parts Find convolution kernel using stars Measure galaxy shapes using kernel –Obtain noisy shear estimate per galaxy Apply statistic –Averages out intrinsic galaxy shapes –e.g. mean shear in circular aperture Predict statistic from theory Calculate  2 between observation and prediction Estimate cosmological parameters

20. Conventional approach: Split into several parts Find convolution kernel using stars Measure galaxy shapes using kernel –Obtain noisy shear estimate per galaxy Apply statistic –Averages out intrinsic galaxy shapes –e.g. mean shear in circular aperture Predict statistic from theory Calculate  2 between observation and prediction Estimate cosmological parameters

21. Weakly Lensed Galaxies

22. 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 Current status: –STEP 1: simplistic galaxy shapes (Heymans et al 2005) –STEP 2: more realistic galaxies (Massey et al 2006) –STEP 3: difficult (space telescope) kernel (2007) –STEP 4: back to basics

23. Heymans et al 2005

24. STEP4 simplifications Kernel is constant across the image –Star positions are known approximately Galaxy positions are known approximately –No overlapping galaxies –Galaxy/star classification known Shear is same for all galaxies Stars and galaxies have elliptical isophotes Noise level constant across the image

25. How STEP4 images are made Decide galaxy, star positions and profiles Convolve galaxies with kernel Pixelise (integrate light over square pixel) Add random Gaussian noise to each pixel ~1,000,000 galaxies in total

26. Kaiser, Squires & Broadhurst 1995 The only currently widely used method Interpolate P sh and P sm using polynomial

27. Shapelets – a popular bet for the future Laguerre polynomials –Nice QM formalism Lensing distortion has simple effect psf convolution can be removed by matrix multiplication Massey & Refregier 2004

28. Our approach Use other software to locate stars and galaxies –chop out e.g. a 16x16 postage stamp Fit a sum of elliptical Gaussians to each star Fit a sum of concentric elliptical Gaussians to each galaxy image –convolved with average shapes of ~5 nearest stars e.g. Bridle, Kneib, Bardeau, Gull 2001

29. Conclusions Cosmic shear → the nature of dark energy / other Images of the sky → cosmic shear The statistics problem is what limits us Cosmic shear community is relatively small Benchmark simulations now exist Many astronomers and cosmologists doubt that these problems will ever be overcome