| Abstract
| - We study the shapes of galaxy dark matter haloes by measuring the anisotropy of the weak gravitational lensing signal around galaxies in the second Red-sequence Cluster Survey (RCS2). We determine the average shear anisotropy within the virial radius for three lens samples: the “all” sample, which contains all galaxies with 19 < mr′ < 21.5, and the “red” and “blue” samples, whose lensing signals are dominated by massive low-redshift early-type and late-type galaxies, respectively. To study the environmental dependence of the lensing signal, we separate each lens sample into an isolated and clustered part and analyse them separately. We address the impact of several complications on the halo ellipticity measurement, including PSF residual systematics in the shape catalogues, multiple deflections, and the clustering of lenses. We estimate that the impact of these is small for our lens selections. Furthermore, we measure the azimuthal dependence of the distribution of physically associated galaxies around the lens samples. We find that these satellites preferentially reside near the major axis of the lenses, and constrain the angle between the major axis of the lens and the average location of the satellites to ⟨ θ⟩ = 43.7° ± 0.3° for the “all” lenses, ⟨ θ⟩ = 41.7° ± 0.5° for the “red” lenses and ⟨ θ⟩ = 42.0° ± 1.4° for the “blue” lenses. We do not detect a significant shear anisotropy for the average “red” and “blue” lenses, although for the most elliptical “red” and “blue” galaxies it is marginally positive and negative, respectively. For the “all” sample, we find that the anisotropy of the galaxy-mass cross-correlation function ⟨ f − f45⟩ = 0.23 ± 0.12, providing weak support for the view that the average galaxy is embedded in, and preferentially aligned with, a triaxial dark matter halo. Assuming an elliptical Navarro-Frenk-White profile, we find that the ratio of the dark matter halo ellipticity and the galaxy ellipticity f h = e h/e g = 1.50 -1.01+1.03, which for a mean lens ellipticity of 0.25 corresponds to a projected halo ellipticity of e h = 0.38 -0.25+0.26 if the halo and the lens are perfectly aligned. For isolated galaxies of the “all” sample, the average shear anisotropy increases to ⟨ f-f45⟩ = 0.51 -0.25+0.26 and fh = 4.73 -2.05+2.17, whilst for clustered galaxies the signal is consistent with zero. These constraints provide lower limits on the average dark matter halo ellipticity, as scatter in the relative position angle between the galaxies and the dark matter haloes is expected to reduce the shear anisotropy by a factor ~2.
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