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 (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)
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)
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)
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
i  Aij 
'
j
g = g1 + ig2
Weak
lensing
to higher
order:
flexion
 =  1 + i 2 '
i 1 A


j
* ij
 = 2  
g = 12 
F = 
G = g
+ Dijk  
'
j
1
2
Spin 1
Spin 2
'
k
Spin 3
Flexion is sensitive to matter variations at
smaller scales than shear
– it’s like a high pass filter for mass structure

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 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 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
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
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…

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()
(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 galaxygalaxy and cosmic flexion signals is
underway; these will place new constraints
upon small-scale dark matter structure