Detection of large scale intrinsic ellipticity-density correlation from the Sloan Digital Sky Survey and implications for weak lensing surveys

TL;DR

This paper uses SDSS spectroscopic galaxies with calibrated SDSS imaging ellipticities to constrain intrinsic alignments that contaminate weak lensing. It finds no significant II correlation but detects a robust GI signal for galaxies brighter than L*, extending to large scales; the result implies that current lensing analyses may underestimate the matter fluctuation amplitude by up to ~20–30% depending on redshift and sample. The authors model the GI signal with both power-law and HRH* forms, explore redshift evolution, and quantify implications for current and upcoming surveys, including the potential benefit of excluding BCGs. The work highlights intrinsic alignments as a critical systematic for precision cosmology with cosmic shear and motivates methodological mitigations and further empirical constraints.

Abstract

The power spectrum of weak lensing shear caused by large-scale structure is an emerging tool for precision cosmology, in particular for measuring the effects of dark energy on the growth of structure at low redshift. One potential source of systematic error is intrinsic alignments of ellipticities of neighbouring galaxies (II correlation) that could mimic the correlations due to lensing. A related possibility pointed out by Hirata and Seljak (2004) is correlation between the intrinsic ellipticities of galaxies and the density field responsible for gravitational lensing shear (GI correlation). We present constraints on both the II and GI correlations using 265 908 spectroscopic galaxies from the SDSS, and using galaxies as tracers of the mass in the case of the GI analysis. The availability of redshifts in the SDSS allows us to select galaxies at small radial separations, which both reduces noise in the intrinsic alignment measurement and suppresses galaxy- galaxy lensing (which otherwise swamps the GI correlation). While we find no detection of the II correlation, our results are nonetheless statistically consistent with recent detections found using the SuperCOSMOS survey. In contrast, we have a clear detection of GI correlation in galaxies brighter than L* that persists to the largest scales probed (60 Mpc/h) and with a sign predicted by theoretical models. This correlation could cause the existing lensing surveys at z~1 to underestimate the linear amplitude of fluctuations by as much as 20% depending on the source sample used, while for surveys at z~0.5 the underestimation may reach 30%. (Abridged.)

Figures (7)

• Figure 1: The correlation functions $w_{g+}(r_p)$, $w_{++}(r_p)$, and $w_{\times\times}(r_p)$ obtained from the L3, L4, L5, L6, and the full galaxy samples. Each of the 10 bins contains the same range in $r_p$ for each of the samples, but some of the error bars have been slightly displaced horizontally for clarity (L5 has not been displaced). The L6 data have been multiplied by 0.1 so that they can fit on the same scale. All the errors are 68 per cent confidence bands, and the errorbars are highly correlated on large scales.
• Figure 2: The correlation functions $w_{g+}(r_p)$, $w_{++}(r_p)$, and $w_{\times\times}(r_p)$ obtained from the L3--L6 galaxy samples. Same as Fig. \ref{['fig:rachel']} except that Pipeline II was used, and results are not shown for the full sample.
• Figure 3: The size of errors of $w_{g+}$ for L3 as a function of $r_p$ for the density-shape correlations, relative to the size of the errors for 50 jackknife regions.
• Figure 4: Power law fits to the intrinsic alignment signal from Pipeline I. From top to bottom, the rows represent the luminosity ranges L3, L4, L5, L6, and the full sample; from left to right, the columns represent the $w_{g+}$, $w_{++}$, and $w_{\times\times}$ correlations respectively. The dots indicate the $\chi^2$ minimum, and the contours represent 75, 95, and 99 per cent confidence regions. In the L6 density-shape plot, there was an insufficient number of pairs in the innermost bin to establish a reliable jackknife error estimate, so this plot is based on only $N=9$ data points.
• Figure 5: The allowed range of GI contamination for each luminosity subsample. The power-law fits are used, with the left column showing the results for the stable clustering assumption and the right column showing the results for linear evolution as argued by 2004PhRvD..70f3526H. The bottom and top curves show the 95 per cent confidence region assuming a power law intrinsic alignment model with index $-3<\alpha_{g+}<+1$. The center curve shows the contamination predicted by the best-fit parameters in Table \ref{['tab:powerlawfits']}. The median source redshift assumed is $z_{med}=1.0$. [The constraints on $\alpha_{g+}$ are imposed because for $\alpha_{g+}\ge +1$ or $\alpha_{g+}\le -4$, the Hankel transform defining $P_{\delta,\tilde{\gamma}^I}(k)$ becomes ill-defined. A cutoff value greater than $-4$ was chosen because otherwise the correlations at very small scales dominates the power spectrum. Note that in the cases of L5 and L6 where we have a detection, $\alpha_{g+}$ is constrained to lie within the range given here at $>99$ per cent confidence.]