Weak Gravitational Flexion from HST GEMS and STAGES

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)

STAGES TEAM GEMS TEAM Hans Walter Rix (PI) (MPIA) Marco Barden (MPIA) Steven Beckwith (STSc. I) 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 Mc. Intosh (UMass) Klaus Meisenheimer (MPIA) Chien Peng (STSc. I) Sebastian Sanchez (CAHA) Rachel Somerville (MPIA) Lutz Wisotzki (AIP) Christian Wolf (Oxford) Xianzhong Zheng (MPIA) 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 Mc. Intosh (UMass) Klaus Meisenheimer (MPIA) Chien Peng (STSc. I) Hans Walter Rix (MPIA) Sebastian Sanchez (CAHA) Rachel Somerville (MPIA) Andy Taylor (Edinburgh) Lutz Wisotzki (AIP) Christian Wolf (Oxford) Xianzhong Zheng (PMO)

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

“Traditional” weak lensing source Image transformations can often be described by a simple, locally linearized mapping: lens observer g = g 1 + i g 2

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

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

Flexion from space We are using the GEMS and STAGES surveys for a combined shear-flexion weak lensing analysis 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).

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 2 D basis functions • All shape information can then be easily quantified Massey et al. 2006

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

Shear and flexion measurements g G F

Quick and dirty “STEP”

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

Galaxy-galaxy shear

Galaxy-galaxy F

Galaxy-galaxy G

Flexion correlation statistics 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. Massive foreground halo Background galaxy Predictions for lensing correlation functions C(q) (for gg, FF, GG etc. ) exist, and can be used to constrain cosmological parameters.

Cosmic flexion F G

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 and cosmic flexion signals is underway; these will place new constraints upon small-scale dark matter structure