Ellipticity of dark matter haloes with galaxy-galaxy weak lensing

We present the results of attempts to detect the ellipticity of dark matter haloes using galaxy-galaxy weak lensing with Sloan Digital Sky Survey (SDSS) data. We use 2 020 256 galaxies brighter than r = 19 with photometric redshifts (divided into colour and luminosity subsamples) as lenses and 31 697 869 source galaxies. We search for and identify several signal contaminants, which if not removed lead to a spurious detection. These include systematic shear that leads to a slight spurious alignment of lens and source ellipticities, intrinsic alignments (due to contamination of the source sample by physically associated lens-source pairs), and anisotropic magnification bias. We develop methods that allow us to remove these contaminants to the signal. We split the analysis into blue (spiral) and red (elliptical) galaxies. Assuming Gaussian errors as in previous work and a power-law profile, we find f(h) = e(h)/e(g) = 0.1 +/- 0.06 for red galaxies and-0.8 +/- 0.4 for blue galaxies, using transverse separations of 20-300 h(-1) kpc, averaged over luminosity. Inclusion of the more realistic non-Gaussian error distributions and of the Navarro-Frenk-White (NFW) density profile (which predicts much smaller ellipticity of the shear for scales above the scale radius) yields 0.60 +/- 0.38 for ellipticals and -1.4(-2.0)(+1.7) for spirals. While there is no concrete detection of alignment in either case, there is a suggestion in the data of a positive alignment in the brightest lens sample of ellipticals. Our results appear to be mildly inconsistent with a previously reported detection by Hoekstra, Yee & Gladders, but more data and further tests are needed to clarify whether the discrepancy is real or a consequence of differences in the lens galaxy samples used and analysis methods.