  Current theories of structure formation predict specific density profiles of
galaxy dark matter haloes, and with weak gravitational lensing we can probe
these profiles on several scales. On small scales, higher-order shape
distortions known as flexion add significant detail to the weak lensing
measurements. We present here the first detection of a galaxy-galaxy flexion
signal in space-based data, obtained using a new Shapelets pipeline introduced
here. We combine this higher-order lensing signal with shear to constrain the
average density profile of the galaxy lenses in the Hubble Space Telescope
COSMOS survey. We also show that light from nearby bright objects can
significantly affect flexion measurements. After correcting for the influence
of lens light, we show that the inclusion of flexion provides tighter
constraints on density profiles than does shear alone. Finally we find an
average density profile consistent with an isothermal sphere.
