We use a series of Monte Carlo simulations to investigate the theory of galaxy-galaxy lensing by non-spherical dark matter haloes. The simulations include a careful accounting of the effects of multiple deflections on the galaxy-galaxy lensing signal. In a typical observational data set where the mean tangential shear of sources with redshifts $z_s \simeq 0.6$ is measured with respect to the observed symmetry axes of foreground galaxies with redshifts $z_l \simeq 0.3$, we find that the signature of anisotropic galaxy-galaxy lensing differs substantially from the simple expectation that one would have in the absence of multiple deflections. In general, the observed ratio of the mean tangential shears, $\gamma^+ (\theta) / \gamma^- (\theta)$, is strongly suppressed compared to the function that one would measure if the intrinsic symmetry axes of the foreground galaxies were known. Depending upon the characteristic masses of the lenses, the observed ratio of the mean tangential shears may be consistent with an isotropic signal (despite the fact that the lenses are non-spherical), or it may even be reversed from the expected signal (i.e., the mean tangential shear for sources close to the observed minor axes of the lenses may exceed the mean tangential shear for sources close to the observed major axes of the lenses). These effects are caused primarily by the fact that the images of the lens galaxies have, themselves, been lensed and therefore the observed symmetry axes of the lens galaxies differ from their intrinsic symmetry axes. We show that the effects of lensing of the foreground galaxies on the observed function $\gamma^+ (\theta) / \gamma^- (\theta)$ cannot be eliminated simply by the rejection of foreground galaxies with very small image ellipticities, nor by simply focusing the analysis on sources that are located very close to the observed symmetry axes of the foreground galaxies. We conclude that any attempt to use a measurement of $\gamma^+ (\theta) / \gamma^- (\theta)$ to constrain the shapes of dark matter galaxy haloes must include Monte Carlo simulations that take multiple deflections properly into account.
Status: accepted for publication in MNRAS
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The frequency and effects of multiple weak deflections in galaxy-galaxy lensing are investigated via Monte Carlo simulations. The lenses in the simulations are galaxies with known redshifts and known rest-frame blue luminosities. The frequency of multiple deflections above a given threshold shear value is quantified for discrete source redshifts, as well as for a set of sources that are broadly distributed in redshift space. In general, the closest lens in projection on the sky is neither the only lens for a given source, nor is it the strongest lens. Compared to a naive single-deflection calculation in which only the lensing due to the closest lens is considered, a full multiple-deflection calculation yields a higher net shear for individual sources, as well as a higher mean tangential shear around the lens centers. The full multiple-deflection calculation also shows that galaxy-galaxy lensing may contribute a substantial amount to cosmic shear on small angular scales. The degree to which galaxy-galaxy lensing contributes to the small-scale cosmic shear is, however, quite sensitive to the mass adopted for the halos of L_B* galaxies. Changing the halo mass by a factor of ~ 2.5 changes the contribution of galaxy-galaxy lensing to the cosmic shear by a factor of ~ 3 on scales of theta ~ 1'. The contribution of galaxy-galaxy lensing to cosmic shear decreases rapidly with angular scale and extrapolates to zero at theta ~ 5'. This last result is roughly independent of the halo mass and suggests that for scales theta > 5', cosmic shear is insensitive to the details of the gravitational potentials of large galaxies.
Status: Published (ApJ, vol. 713, pgs. 603-614, 2010)
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We investigate the locations of the satellites of relatively isolated host galaxies in the Sloan Digital Sky Survey and the Millennium Run simulation. Provided we use two distinct prescriptions to embed luminous galaxies within the simulated dark matter halos (ellipticals share the shapes of their halos, while disks have angular momenta that are aligned with the net angular momenta of their halos), we find a fair agreement between observation and theory. Averaged over scales rp <= 500 kpc, the satellites of red, high-mass hosts with low star formation rates are found preferentially near the major axes of their hosts. In contrast, the satellites of blue, low-mass hosts with low star formation rates show little to no anisotropy when averaged over the same scale. The difference between the locations of the satellites of red and blue hosts cannot be explained by the effects of interlopers in the data. Instead, it is caused primarily by marked differences in the dependence of the mean satellite location, < phi >, on the projected distance at which the satellites are found. We also find that the locations of red, high-mass satellites with low star formation rates show considerably more anisotropy than do the locations of blue, low-mass satellites with high star formation rates. There are two contributors to this result. First, the blue satellites have only recently arrived within their hosts' halos, while the red satellites arrived in the far distant past. Second, the sample of blue satellites is heavily contaminated by interlopers, which suppresses the measured anisotropy compared to the intrinsic anisotropy.
Status: Published (ApJ, vol. 709, pgs. 1321-1336, 2010)
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We compute the two-point image correlation function for bright galaxies in the seventh data release of the Sloan Digital Sky Survey (SDSS) over angular scales 0.01' <= theta <= 120' and projected separations 0.01 Mpc <= rp <= 10 Mpc. We restrict our analysis to SDSS galaxies with accurate spectroscopic redshifts, and we find strong evidence for intrinsic alignment of the galaxy images. On scales greater than rp ~ 40 kpc, the intrinsic alignment of the SDSS galaxy images compares well with the intrinsic alignment of galaxy images in a LCDM universe, provided we impose Gaussian-random errors on the position angles of the theoretical galaxies with a dispersion of 25 degrees. Without the inclusion of these errors, the amplitude of the two-point image correlation function for the theoretical galaxies is a factor of order 2 higher than it is for the SDSS galaxies. We interpret this as a combination of modest position angle errors for the SDSS galaxies, as well as a need for modest misalignment of mass and light in the theoretical galaxies. The intrinsic alignment of the SDSS galaxies shows no dependence on the specific star formation rates of the galaxies and, at most, a very weak dependence on the colors and stellar masses of the galaxies. At the ~ 3 sigma level, however, we find an indication that the images of the most luminous SDSS galaxies are more strongly aligned with each other than are the images of the least luminous SDSS galaxies.
Status: submitted to ApJ, in revision
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