Weak Gravitational Flexionfrom HST GEMS and

STAGESBarnaby Rowe

with David Bacon (Portsmouth), Andy Taylor (Edinburgh),

Catherine Heymans (U.B.C.), Richard Massey (Caltech),Dave Goldberg (Drexel)

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

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…

“Traditional” weak lensing

source

lens

observer

1i2'jiji A

Image transformations can often be described by a simple, locally linearized mapping:

''21'

kjijkjiji DA

Weak lensing to higher order: flexion

GF

i

21

*21

21

Spin 1 Spin 3Spin 2

x

Flexion is sensitive to matter variations atsmaller 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

We are using the GEMS and STAGES surveys for a combined shear-flexion weak lensing analysis

Flexion from space

The fields each offer:

• >800 arcmin2 of deep (~60 galaxies per arcmin2) space imaging from the HST-ACS.

• >8 000 high-quality photometric redshifts from the COMBO-17 survey (see Wolf et al. 2004).

Measuring galaxy shapesWe 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

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

F

Quick and dirty “STEP”

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

Galaxy-galaxy shear

Galaxy-galaxy F

Galaxy-galaxy G

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

Backgroundgalaxy

Predictions for lensing correlation functions C() (for , 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-galaxy and cosmic flexion signals is underway; these will place new constraints upon small-scale dark matter structure