Spin induced galaxy alignments and their implications for weak lensing measurements

Abstract

Large scale correlations in the orientations of galaxies can result from alignments in their angular momentum vectors. These alignments arise from the tidal torques exerted on neighboring proto-galaxies by the smoothly varying shear field. We compute the predicted amplitude of such ellipticity correlations using the Zel'dovich approximation for a realistic distribution of galaxy shapes. Weak gravitational lensing can also induce ellipticity correlations since the images of neighboring galaxies will be distorted coherently. On comparing these two effects that induce shape correlations, we find that for current weak lensing surveys with a median redshift of z_m = 1, the intrinsic signal is of order 1 - 10 percent of the measured signal. However, for shallower surveys with z_m < 0.3, the intrinsic correlations dominate over the lensing signal. The distortions induced by lensing are curl-free, whereas those resulting from intrinsic alignments are not. This difference can be used to disentangle these two sources of ellipticity correlations.

Figures (5)

• Figure 1: Left panel: The average ellipticities of the different morphological types of galaxies seen from a given angle $\theta$ with respect to the angular momentum vector. Also shown is the result for a sample with all types weighted by the observed fractions in the APM survey. All scale roughly as the thin disk case, Right panel: The distribution of ellipticities for the different morphological types based on the LBL intrinsic shape distributions. The differences between the LBL model and the fit from lensing surveys (dashed curve) could either be due to there being a different morphological mix in high redshift surveys or evolution in the intrinsic shape distributions, particularly for the spirals.
• Figure 2: Left panel: The computed three dimensional ellipticity correlation function averaged over angles and plotted as a function of separation. The signal is appreciable at separations smaller than the smoothing scale ($< 1$ Mpc) and falls off as $\xi^2(r)$. For comparison we have plotted the exact derived function [solid curve] against the approximation of Equation (\ref{['eqn:rough']}) [dashed curve]. Right panel: The expectation value of the two components of the two point ellipticity correlation $\langle \epsilon_+ \epsilon_+\rangle$ and $\langle\epsilon_{\times} \epsilon_{\times}\rangle$ divided by the approximate curve (solid curve of left panel) for various values of the viewing angle $\theta = 0, \pi/4$ and $\pi/2$ are shown. Note that the 2 components are equal for $\theta = 0$.
• Figure 3: The angle averaged ellipticity correlations from Gaussian field realizations on a $512^3$ grid compared to the analytic results. The correlations at peaks of the density field (shown as solid squares) appear to match well with the results from random positions (the dot-dashed line). At zero-lag they both asymptote to the exact result ($1/60$) shown by the horizontal dot-dashed line. The full analytic correlations (solid curves) as well as the analytic estimate where the large scale power has been removed (dashed curve) to account for the finite size of the realizations are both shown. These are not valid below the smoothing scale. The analytic results match well in the region where they are valid, i. e. at scales larger than the smoothing length, but note the importance of large-scale power (here we have set $a=\alpha=1$).
• Figure 4: The projected 2-d ellipticity correlation functions, $\xi_+$ and $\xi_\times$, for various values of the median redshift of the distribution of galaxies. Here we have assumed the galaxies are well described by thin disks and are perfectly aligned with the linear predictions ($a=\alpha=1$.) but deviate at larger separation. Both increase strongly with decreasing redshift, roughly proportional to $z_m^{-2}$.
• Figure 5: The intrinsic correlation signal versus the predictions from weak lensing and current observations. Left panel: $\xi_+(\theta)+\xi_\times(\theta)$ for a median redshift of 1, compared to the measured shear correlation function. At small separations, the intrinsic signal is approximately one percent of the measured value. The amplitude depends on the value of the assumed average galaxy thickness ($\alpha$) and the parameter $a$ that describes how well the angular momentum of the galaxy is correlated with the shear field. We plot $a=0.24$ (full line) and $a=0.55$ (short-dashed line) which correspond to the values inferred from numerical simulations by LP00 and Heavens et al. (2000) respectively. $\alpha=0.73$ corresponds to the value determined from the observed distribution of ellipticities (Ebbels et al. 2000). The data are: van Waerbeke et al. (2000) -- solid squares ; Wittman et al. (2000) -- filled circles ; Kaiser et al. (2000) -- open circles; and Bacon et al. (2000) -- filled triangle. The long-dashed line is the theoretical prediction from Jain & Seljak (1997) computed for a $\Omega_\Lambda=0.7$ galaxy cluster normalized flat universe, $\sim 4.75\times10^{-4}(\theta/{\rm arc min})^{-0.84}$. Right panel: as in the left panel but for the predictions for a shallower survey such as SDSS and 2dF with median redshift $z_m=0.1$. The intrinsic signal is again shown for two values of $a$, and the theoretical prediction for weak lensing is the long-dashed line (for $z_m=0.1$) and dotted-long-dashed (for $z_m=0.5$). The lensing prediction for $z_m=0.1$ is extrapolated from the Jain & Seljak fit beyond the stated range of validity. For such low redshifts, the intrinsic signal is significant and may dominate over the lensing contribution for most scales.