1. Weak Gravitational Flexion from HST GEMS and STAGES Barnaby Rowe with David Bacon (Portsmouth), Andy Taylor (Edinburgh), Catherine Heymans (U.B.C.), Richard Massey (Caltech), Dave Goldberg (Drexel)

2. Meghan Gray (PI) (Nottingham) David Bacon (Portsmouth) Michael Balogh (Waterloo) Marco Barden (MPIA) Fabio Barazza (UTexas) Eric Bell (MPIA) Asmus Boehm (AIP) John Caldwell (UTexas) Boris Häußler (MPIA) Catherine Heymans (UBC) Knud Jahnke (MPIA) Shardha Jogee (UTexas) Eelco van Kampen (Innsbruck) Sergey Koposov (MPIA) Kyle Lane (Nottingham) Daniel McIntosh (UMass) Klaus Meisenheimer (MPIA) Chien Peng (STScI) Hans Walter Rix (MPIA) Sebastian Sanchez (CAHA) Rachel Somerville (MPIA) Andy Taylor (Edinburgh) Lutz Wisotzki (AIP) Christian Wolf (Oxford) Xianzhong Zheng (PMO) Hans Walter Rix (PI) (MPIA) Marco Barden (MPIA) Steven Beckwith (STScI) Eric Bell (MPIA) Andrea Borch (MPIA) John Caldwell (UTexas) Boris Häußler (MPIA) Catherine Heymans (UBC) Knud Jahnke (MPIA) Shardha Jogee (UTexas) Sergey Koposov (MPIA) Daniel McIntosh (UMass) Klaus Meisenheimer (MPIA) Chien Peng (STScI) Sebastian Sanchez (CAHA) Rachel Somerville (MPIA) Lutz Wisotzki (AIP) Christian Wolf (Oxford) Xianzhong Zheng (MPIA) STAGES TEAM GEMS TEAM

3. Simulations exhibit an abundance of dark matter substructure at a wide range of scales… …they also suggest that halos follow a certain profile (e.g. the NFW density profile – see Navarro, Frenk & White 1997) (Moore et al. 1999) Cluster halo Galaxy halo …but these predictions remain untested Detailed predictions exist for halo properties and substructure as a function of mass, formation time and environment…

4. “Traditional” weak lensing source lens observer   1  i  2 Image transformations can often be described by a simple, locally linearized mapping:

5. Weak lensing to higher order: flexion Spin 1Spin 3Spin 2

6.  x Flexion is sensitive to matter variations at smaller scales than shear – it’s like a high pass filter for mass structure Cosmological predictions (see Bacon et al. 2006) show that flexion is particularly sensitive to dark matter structure at small scales

7. We are using the GEMS and STAGES surveys for a combined shear-flexion weak lensing analysis Flexion from space The fields each offer: >800 arcmin 2 of deep (~60 galaxies per arcmin 2 ) space imaging from the HST-ACS. >8 000 high-quality photometric redshifts from the COMBO-17 survey (see Wolf et al. 2004).

8. Measuring galaxy shapes We can make accurate measurements of galaxy shapes using the Shapelet formalism (see e.g. Refregier 2003, Massey & Refregier 2005) Using this method we can decompose each image into a sum of orthogonal 2D basis functions All shape information can then be easily quantified Massey et al. 2006

9. PSF correction We built a detailed shapelet model of each star Using these models we can estimate the PSF across the survey images– then deconvolve our galaxies in shapelet space

10. Shear and flexion measurements G  F

11. Quick and dirty “STEP”

12. Galaxy-galaxy lensing is a useful tool for studying galaxy halo mass distributions lens galaxy source galaxy  For shear, we may first look at the mean tangential shear within angular bins around foreground lenses… For flexion the median provides a better statistic, being less sensitive to the broad wings in F and G

13. Galaxy-galaxy shear

14. Galaxy-galaxy F

15. Galaxy-galaxy G

16. In a Universe in which matter is correlated (clumpy) we also expect correlations between the shears and flexions of pairs of galaxies, varying as a function of angular separation. Flexion correlation statistics Massive foreground halo Background galaxy Predictions for lensing correlation functions C(  ) (for , FF, GG etc.) exist, and can be used to constrain cosmological parameters.

17. Cosmic flexion FG

18. Summary Flexion is a promising tool for studying dark matter structure on small scales Measurements of flexion from HST GEMS and STAGES demonstrate that the signal can be accurately recovered Maximum-likelihood analysis of galaxy- galaxy and cosmic flexion signals is underway; these will place new constraints upon small-scale dark matter structure