Intrinsic Correlation of Galaxy Shapes: Implications for Weak Lensing Measurements

TL;DR

The paper quantifies intrinsic galaxy shape correlations arising from halo spin alignments and assesses their impact on weak lensing. Using large N-body halo catalogs, it models spiral disks perpendicular to halo angular momentum and an elliptical-halo model, deriving projected ellipticity correlations. The intrinsic signal is typically smaller than the weak-lensing signal for deep surveys (about $10^{-4}$ on arcminute scales, dropping to $10^{-5}$ at larger angles) but could dominate in shallow, wide surveys, underscoring the need for calibration and separate angular signatures. Overall, intrinsic alignments are a contaminant that is manageable for deep lensing while offering insights into galaxy formation physics and potential constraints on halo spin correlations.

Abstract

Weak gravitational lensing is now established as a powerful method to measure mass fluctuations in the universe. It relies on the measurement of small coherent distortions of the images of background galaxies. Even low-level correlations in the intrinsic shapes of galaxies could however produce a significant spurious lensing signal. These correlations are also interesting in their own right, since their detection would constrain models of galaxy formation. Using $3\times 10^{4} - 10^5$ halos found in N-body simulations, we compute the correlation functions of the intrinsic ellipticity of spiral galaxies assuming that the disk is perpendicular to the angular momentum of the dark matter halo. We also consider a simple model for elliptical galaxies, in which the shape of the dark matter halo is assumed to be the same as that of the light. For deep lensing surveys with median redshifts $\sim 1$, we find that intrinsic correlations of $\sim 10^{-4}$ on angular scales $θ\sim 0.1-10'$ are generally below the expected lensing signal, and contribute only a small fraction of the excess signals reported on these scales. On larger scales we find limits to the intrinsic correlation function at a level $\sim 10^{-5}$, which gives a (model-dependent) range of separations for which the intrinsic signal is about an order of magnitude below the ellipticity correlation function expected from weak lensing. Intrinsic correlations are thus negligible on these scales for dedicated weak lensing surveys. For wider but shallower surveys such as SuperCOSMOS, APM and SDSS, we cannot exclude the possibility that intrinsic correlations could dominate the lensing signal. We discuss how such surveys could be used to calibrate the importance of this effect, as well as study spin-spin correlations of spiral galaxies.

Figures (7)

• Figure 1: Geometry of the ellipticity correlation functions. Two galaxies separated by an angle $\theta$ are assigned ellipticities $\epsilon_{i}(0)$ and $\epsilon_{i}(\theta)$. These ellipticities can then be transformed into the rotated ellipticities $\epsilon_{i}^{r}(0)$ and $\epsilon_{i}^{r}(\theta)$ defined in the coordinate system (thin solid lines) which is aligned with the separation vector ${\mathbf \theta}$. The two correlation functions are then defined as $C_{1}(\theta) \equiv \langle \epsilon_{1}^{r}(0) \epsilon_{1}^{r}(\theta) \rangle$ and $C_{2}(\theta) \equiv \langle \epsilon_{2}^{r}(0) \epsilon_{2}^{r}(\theta) \rangle$
• Figure 2: Intrinsic ellipticity correlation functions $|C_{1}(\theta)|$ (top group) and $|C_{2}(\theta)|$ (bottom group) for spiral galaxies, for each cosmological model. The correlation functions expected from lensing are shown as dotted lines. The source redshift was taken to be $z_{s}=1$, corresponding to current dedicated weak lensing surveys. Note that error bars are correlated.
• Figure 3: Same as the top group of the previous figure, but for a median galaxy redshift of $z_{m}=0.2$, as appropriate for wide shallower surveys such as SDSS. We have too few small-separation pairs to constrain the intrinsic correlations between close pairs on the sky in a shallow survey. Note that error bars are correlated; most of the estimate comes from the first two bins in 3D, and the final panel is not a significant detection, since it is a log scale.
• Figure 4: Mass histograms for the halos in the 4 model boxes, with 50 bins equally-spaced logarithmically. Minimum mass is set by requiring halos to have at least 10 particles. The maximum mass we consider in the analysis is $10^{13} h^{-1}M_\odot$.
• Figure 5: Simple model of a spiral galaxy which is taken to be a thin disk perpendicular to its angular momentum vector ${\mathbf L}$. The coordinate system is chosen so that the sky is in the $x$-$y$ plane and the line of sight is along the $z$-axis. The disk of the galaxy is shown as the open ellipse, and its projection on the sky as the filled ellipse.